tag:blogger.com,1999:blog-37511821437480075302024-03-13T06:20:27.641-07:00Movimiento parabólicokrissia Urrutiahttp://www.blogger.com/profile/04518663748184719067noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3751182143748007530.post-63856288505837038222009-10-14T19:53:00.000-07:002009-10-18T10:07:04.247-07:00<h1 id="firstHeading" class="firstHeading">Movimiento parabólico</h1>
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trayectoria describe una </span></a><a style="color: rgb(0, 0, 0);" href="http://es.wikipedia.org/wiki/Par%C3%83%C6%92%C3%82%C2%A1bola_%28matem%C3%83%C6%92%C3%82%C2%A1tica%29" title="Parábola (matemática)"><span style="text-decoration: none;">parábola</span></a><span style="color: rgb(0, 0, 0);">. Se corresponde con la trayectoria ideal de un </span><a style="color: rgb(0, 0, 0);" href="http://es.wikipedia.org/wiki/Proyectil" title="Proyectil"><span style="text-decoration: none;">proyectil</span></a><span style="color: rgb(0, 0, 0);"> que se mueve en un medio que no ofrece resistencia al avance y que está sujeto a un </span><a style="color: rgb(0, 0, 0);" href="http://es.wikipedia.org/wiki/Campo_gravitatorio" title="Campo gravitatorio"><span style="text-decoration: none;">campo gravitatorio</span></a> uniforme.<o:p></o:p></span></p><div> </div><p style="font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:verdana;" class="MsoNormal"><span style="line-height: 115%;font-size:130%;" ><o:p> </o:p></span></p><div style="text-align: justify;"> <span style="font-weight: bold; font-style: italic; color: rgb(0, 0, 0);font-family:verdana;font-size:130%;" ><span style="color: rgb(0, 0, 0);font-size:130%;" ><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_edwYt7TL0fw/StaeN1LrxYI/AAAAAAAAABU/J8jAv_c_bzk/s1600-h/images.jpg"><img style="margin: 0pt 0pt 10px 10px; width: 166px; float: right; height: 166px; cursor: pointer;" id="BLOGGER_PHOTO_ID_5392671564274320770" alt="" src="http://3.bp.blogspot.com/_edwYt7TL0fw/StaeN1LrxYI/AAAAAAAAABU/J8jAv_c_bzk/s320/images.jpg" border="0" /></a></span></span>
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div.Section1 {page:Section1;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} </style> <![endif]--><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:verdana;font-size:130%;" ><span style="line-height: 115%;">Puede ser analizado como la composición de dos movimientos rectilíneos: un <a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%83%C6%92%C3%82%C2%ADneo_uniforme" title="Movimiento rectilíneo uniforme"><span style="text-decoration: none; color: rgb(0, 0, 0);">movimiento rectilíneo uniforme</span></a> horizontal y un <a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%83%C6%92%C3%82%C2%ADneo_uniformemente_acelerado" title="Movimiento rectilíneo uniformemente acelerado"><span style="text-decoration: none; color: rgb(0, 0, 0);">movimiento re</span></a><a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%83%C6%92%C3%82%C2%ADneo_uniformemente_acelerado" title="Movimiento rectilíneo uniformemente acelerado"><span style="text-decoration: none; color: rgb(0, 0, 0);">ctilíneo u</span></a><a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%83%C6%92%C3%82%C2%ADneo_uniformemente_acelerado" title="Movimiento rectilíneo uniformemente acelerado"><span style="text-decoration: none; color: rgb(0, 0, 0);">niformemente acelerado</span></a> 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<br /></span></p><div style="text-align: justify;"> </div><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:verdana;"><span style="font-size:130%;"><span style="">OBJETIVOS<o:p style="font-weight: normal;"></o:p></span></span></p><div style="text-align: justify; color: rgb(0, 0, 0);"> </div><p class="MsoNormal" style="margin-left: 36pt; text-indent: -18pt; font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:verdana;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="line-height: 115%;"><span style="">1. </span></span><span style="line-height: 115%;">Estudiar los conceptos básicos del movimiento parabólico descrito en la experiencia realizada en el laboratorio.<o:p></o:p></span></span><!--[endif]--></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 36pt; text-indent: -18pt; font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:verdana;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="line-height: 115%;"><span style="">2.<span style=""> </span></span></span><span style="line-height: 115%; font-weight: bold;">Describir las características del movimiento parabólico que realiza el balín.<o:p></o:p></span></span><!--[endif]--></p><div style="text-align: justify; font-weight: bold;"> </div><p class="MsoNormal" style="margin-left: 36pt; text-indent: -18pt; font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:verdana;"><!--[if !supportLists]--><span style="font-size:130%;"><span style="line-height: 115%;"><span style="">3.<span style=""> </span></span></span><span style="line-height: 115%;">Desarrollar los conceptos de velocidad, distancia y gravedad descritos por el movimiento y la distancia del balín al ser lanzados hacia distancias cada vez mayores.<o:p></o:p></span></span><!--[endif]--></p><div style="text-align: justify;"> </div><p 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href="http://www.monografias.com/trabajos11/basda/basda.shtml"><span style="text-decoration: none; color: rgb(0, 0, 0);">datos</span></a> el movimiento y determinar su <a href="http://www.monografias.com/trabajos16/comportamiento-humano/comportamiento-humano.shtml" id="autolink"><span style="text-decoration: none; color: rgb(0, 0, 0);">comportamiento</span></a> con respecto al plano coordenado (abscisa x, ordenada y)<o:p></o:p></span><!--[endif]--></p><div style="text-align: justify;"> </div><p style="font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:georgia;"><span style="font-size:130%;"><span style=""><o:p> </o:p></span></span></p><div style="text-align: justify;"> </div><p style="font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: center;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><span style="line-height: 115%;"> <!--[if !supportLineBreakNewLine]--> <!--[endif]--></span><o:p></o:p>
<br /></span></p><p style="color: rgb(0, 0, 0); text-align: center; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">Tipos de movimiento parabólico<o:p></o:p></span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; font-weight: bold; font-style: italic; color: rgb(0, 0, 0); text-align: justify;font-family:verdana;"><span style="font-size:130%;"><o:p> </o:p></span></p><div style="text-align: justify;">
<br /><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:verdana;font-size:130%;" ><span style="line-height: 115%;">Movimiento de media parábola</span></span><span style="font-size:130%;">
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<br /></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:verdana;font-size:130%;" ><span style="line-height: 115%;">El movimiento de media parábola o semiparabólico (lanzamiento horizontal)</span></span><span style="font-size:130%;">
<br /></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:verdana;font-size:130%;" ><span style="line-height: 115%;">se puede considerar como la composición de un avance horizontal rectilíneo uniforme y la caída libre</span></span></div><div style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;" class="thumb tright"><div style="width: 262px;" class="thumbinner"><span style="font-size:130%;"><a class="image" href="http://es.wikipedia.org/wiki/Archivo:Rzutp.gif"><img class="thumbimage" alt="" src="http://upload.wikimedia.org/wikipedia/commons/a/ad/Rzutp.gif" width="260" height="189" /></a></span> <div class="thumbcaption"><div class="magnify"><span style="font-size:130%;"><a class="internal" title="Aumentar" href="http://es.wikipedia.org/wiki/Archivo:Rzutp.gif"><img alt="" src="http://es.wikipedia.org/skins-1.5/common/images/magnify-clip.png" width="15" height="11" /></a></span></div><span style="font-size:130%;">
<br /></span><div style="text-align: center;"><span style="font-size:130%;"><span style="font-family:verdana;">Movimiento de media parábola</span>
<br />
<br /></span></div></div></div></div><div style="text-align: justify;"><div style="text-align: justify; font-weight: bold;font-family:verdana;"><span style="color: rgb(0, 0, 0);font-family:verdana;font-size:130%;" ><span>El movimiento parabólico completo</span></span><span style="font-size:130%;">
<br /></span><span style="color: rgb(0, 0, 0);font-family:verdana;font-size:130%;" ><span>puede considerar como la composición de un avance horizontal rectilíneo uniforme y un lanzamiento vertical hacia arriba, que es un movimiento rectilíneo uniformemente acelerado hacia abajo (MRUA) por la acción de la gravedad.</span></span><span style="font-size:130%;">
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<br /><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" ><span>E</span></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>n </span></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>condiciones </span></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>ideales de resistencia al avance nulo y campo gravitatorio uniforme, lo anterior implica que:</span></span><span style="font-size:130%;">
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<br /><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>1. U<span style="font-family:verdana;">n cuerpo que se deja caer libremente y otro que es lanzado horizontalmente desde la misma altura tardan lo mismo en llegar al suelo.</span></span></span>
<br /><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" ><span>2. </span></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>La independencia de la masa en la caída libre y el lanzamiento vertical es igual de válida en los movimientos parabólicos.</span></span><span style="font-weight: bold;font-family:verdana;font-size:130%;" >
<br /></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" ><span>3. Un cuerpo lanzado verticalmente hacia arriba y otro parabólicamente completo que alcance la misma altura tarda lo mismo en caer</span></span><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" ><span>.</span></span>
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<br /><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >Ecuaciones del movimiento parabólico<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_edwYt7TL0fw/StafZhqbLOI/AAAAAAAAABc/o7LezOEpWgE/s1600-h/im.jpg"><img style="margin: 0pt 0pt 10px 10px; width: 237px; float: right; height: 228px; cursor: pointer;" id="BLOGGER_PHOTO_ID_5392672864704605410" alt="" src="http://2.bp.blogspot.com/_edwYt7TL0fw/StafZhqbLOI/AAAAAAAAABc/o7LezOEpWgE/s320/im.jpg" border="0" /></a></span><span style="font-size:130%;">
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<br /></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >Hay dos ecuaciones que rigen el movimiento parabólico:</span>
<br /></div><ol style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><li><span style="font-size:130%;"><img class="tex" alt=" \mathbf{v_0} = v_0 \, \cos{\phi} \, \mathbf{i} + v_0 \, \sin{\phi} \, \mathbf{j} " src="http://upload.wikimedia.org/math/8/f/4/8f4bc8d7f31a8768cca49eb6beaa9b5a.png" /></span></li><li><span style="font-size:130%;"><img class="tex" alt=" \mathbf{a} = -g \, \mathbf{j} " src="http://upload.wikimedia.org/math/c/f/4/cf43643028de8775b58a598b528d3b03.png" /></span> </li></ol><div style="text-align: justify;"><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >donde</span><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" >:</span>
<br /></div><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-size:130%;"><img class="tex" alt=" v_0 \, " src="http://upload.wikimedia.org/math/c/5/e/c5eb8f651f38a8f36ebc1f32de8d7548.png" /> e<span style="font-family:verdana;">s el módulo de la velocidad inicial.</span></span></dd><dd style="font-family:verdana;"><span style="font-size:130%;"><img class="tex" alt=" \phi \, " src="http://upload.wikimedia.org/math/c/d/0/cd014731964c742c274df08d7cc238fb.png" /> es el ángulo de la velocidad inicial sobre la horizontal.</span></dd><dd style="font-family:verdana;"><span style="font-size:130%;"><img class="tex" alt=" g \, " src="http://upload.wikimedia.org/math/f/3/1/f31f123f5b510e1c58b2be1990dcada8.png" /> es la aceleración de la gravedad.</span></dd></dl><div style="text-align: justify; font-weight: bold;font-family:verdana;"><span style="color: rgb(0, 0, 0);font-size:130%;" >La velocidad inicial se compone de dos partes: </span></div><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-size:130%;"><img class="tex" alt=" v_0 \, \cos{\phi} " src="http://upload.wikimedia.org/math/1/7/b/17bd437d16edeaeb342d0fc5514f2564.png" /> que se denomina componente horizontal de la velocidad inicial. </span><dl><dd><span style="font-size:130%;">En lo sucesivo <img class="tex" alt=" v_{0x} \, " src="http://upload.wikimedia.org/math/c/f/2/cf2e9b0137a33b6776a3e45b15dc657b.png" /></span></dd></dl></dd></dl><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-size:130%;"><img class="tex" alt=" v_0 \, \sin{\phi} " src="http://upload.wikimedia.org/math/7/a/3/7a3110e02b357b16fa2b32ba88d409cb.png" /> que se denomina componente vertical de la velocidad inicial. </span><dl><dd><span style="font-size:130%;">En lo sucesiv<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_edwYt7TL0fw/StadjrmrvcI/AAAAAAAAABM/vCOYeUCslb8/s1600-h/Casting_obliquely.gif"><img style="margin: 0pt 10px 10px 0pt; width: 265px; float: left; height: 297px; cursor: pointer;" id="BLOGGER_PHOTO_ID_5392670840148704706" alt="" src="http://2.bp.blogspot.com/_edwYt7TL0fw/StadjrmrvcI/AAAAAAAAABM/vCOYeUCslb8/s320/Casting_obliquely.gif" border="0" /></a>o <img class="tex" alt=" v_{0y} \, " src="http://upload.wikimedia.org/math/a/3/c/a3c0a25a73362b0ee2c0adfe94829cf8.png" /></span></dd></dl></dd></dl><div style="text-align: justify;"><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" >La velocidad inicial se compone de dos partes: </span></div><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-size:130%;"><img class="tex" alt=" v_0 \, \cos{\phi} " src="http://upload.wikimedia.org/math/1/7/b/17bd437d16edeaeb342d0fc5514f2564.png" /> que se denomina componente horizontal de la velocidad inicial. </span><dl><dd><span style="font-size:130%;">En lo sucesivo <img class="tex" alt=" v_{0x} \, " src="http://upload.wikimedia.org/math/c/f/2/cf2e9b0137a33b6776a3e45b15dc657b.png" /></span></dd></dl></dd></dl><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-weight: bold;font-size:130%;" ><img class="tex" alt=" v_0 \, \sin{\phi} " src="http://upload.wikimedia.org/math/7/a/3/7a3110e02b357b16fa2b32ba88d409cb.png" /> que se denomina componente vertical de la velocidad inicial. </span><dl><dd><span style="font-size:130%;"><span style="font-weight: bold;">En lo sucesivo </span><img class="tex" alt=" v_{0y} \, " src="http://upload.wikimedia.org/math/a/3/c/a3c0a25a73362b0ee2c0adfe94829cf8.png" /></span></dd></dl></dd></dl><div style="text-align: justify;">
<br /><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >Será </span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >la que se utilice, excepto en los casos en los que deba tenerse en cuenta el áng ulo de la velocidad inicial.</span>
<br /><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" >
<br /></span><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:georgia;font-size:130%;" >Ecuación de la aceleración </span>
<br />
<br /></div><p style="font-weight: bold; color: rgb(0, 0, 0); text-align: justify;font-family:georgia;"><span style="font-size:130%;">La única aceleración que interviene en este movimiento es la de la gravedad, que corresponde a la ecuación:</span></p><dl style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><dd><span style="font-size:130%;"><img class="tex" alt=" \mathbf{a} = -g \, \mathbf{j} " src="http://upload.wikimedia.org/math/c/f/4/cf43643028de8775b58a598b528d3b03.png" /></span></dd></dl><div style="text-align: justify;"><span style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;font-size:130%;" >q</span><span style="color: rgb(0, 0, 0); font-style: italic; font-weight: bold;font-family:georgia;font-size:130%;" ><span style="font-family:verdana;">ue es vertical y hacia abajo.</span></span>
<br /></div><h3 style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span id="Ecuaci.C3.B3n_de_la_velocidad" class="mw-headline" style="font-size:130%;">Ecuación de la velocidad</span></h3><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">La velocidad de un cuerpo que sigue una trayectoria parabólica se puede obtener integrando la siguiente ecuación:</span></p><h1 style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" id="firstHeading" class="firstHeading"><span style="font-size:130%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_edwYt7TL0fw/StabrfUklCI/AAAAAAAAAA8/Q6rvCgHmgX0/s1600-h/200px-Trajectoria_parab%C3%83%C6%92%C3%82%C2%B2lica.jpg"><img style="margin: 0pt 0pt 10px 10px; width: 150px; float: right; height: 201px; cursor: pointer;" id="BLOGGER_PHOTO_ID_5392668775267210274" alt="" src="http://2.bp.blogspot.com/_edwYt7TL0fw/StabrfUklCI/AAAAAAAAAA8/Q6rvCgHmgX0/s320/200px-Trajectoria_parab%C3%B2lica.jpg" border="0" /></a></span></h1><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">La integración es muy sencilla por tratarse de una <a class="mw-redirect" title="Ecuación diferencial de primer orden" href="http://es.wikipedia.org/wiki/Ecuaci%C3%83%C6%92%C3%82%C2%B3n_diferencial_de_primer_orden">ecuación diferencial de primer orden</a> y el resultado final es:</span></p><div style="text-align: justify;"><blockquote style="padding: 5px 10px; text-align: left; margin-bottom: 0.8em; margin-left: 30px; font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;"><p><span style="font-size:130%;"><img class="tex" alt=" \mathbf{v}(t) = v_{0x}\mathbf{i}+(v_{0y}-gt)\mathbf{j}" src="http://upload.wikimedia.org/math/d/e/9/de95002fe8188369fb4be2ce3a2c56a0.png" /></span></p><p align="justify" style="font-family:verdana;"><span style="font-size:130%;">Cuando un objeto es lanzado con cierta inclinación respecto a la horizontal y bajo la acción solamente de la fuerza gravitatoria su trayectoria se mantiene en el plano vertical y es parabólica.</span></p><p align="center"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/catapult.gif" width="600" height="73" /></span></p><p style="text-align: center;"><span style="font-size:130%;">
<br /></span></p><p style="text-align: center; font-weight: bold;font-family:verdana;"><span style="font-size:130%;">EJEMPLOS </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3"><span style="font-size:130%;">Se patea un balón de fútbol con un ángulo de 37° con una velocidad de 20 m/s. Calcule: </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3"><span style="font-size:130%;">a) La altura máxima. </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3"><span style="font-size:130%;">b) El tiempo que permanece en el aire. </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3"><span style="font-size:130%;">c) La distancia a la que llega al suelo. </span></p><p class="Estilo3"><span style="font-size:130%;">d) La velocidad en X y Y del proyectil después de 1 seg de haber sido disparado </span></p><p class="Estilo3" align="center"><span style="font-size:130%;"><strong>Datos </strong></span></p><table width="282" align="center"><tbody><tr class="Estilo3"><td width="94"><div align="left"><span style="font-size:130%;">Ángulo = 37</span><span class="Estilo3" style="font-size:130%;">°</span></div></td><td width="94"><div align="left"><span style="font-size:130%;">a) Ymax = ? </span></div></td><td width="78"><div align="left"><span style="font-size:130%;">d) Vx =? </span></div></td></tr><tr class="Estilo3"><td><div align="left"><span style="font-size:130%;">Vo = 20m/s </span></div></td><td><div align="left"><span style="font-size:130%;">b) t total = ? </span></div></td><td><div align="left"><span style="font-size:130%;">Vy = ? </span></div></td></tr><tr class="Estilo3"><td><div align="left"><span style="font-size:130%;">g= -9.8 m/s^2 </span></div></td><td><div align="left"><span style="font-size:130%;">c) X = ? </span></div></td><td><span style="font-size:130%;">
<br /></span></td></tr></tbody></table><p class="Estilo3" align="center"><span style="font-size:130%;"><strong><em>Paso 1</em> <img src="http://genesis.uag.mx/edmedia/material/fisica/mov7.jpg" width="140" align="top" height="61" /></strong></span></p><p class="Estilo3" align="center"><span style="font-size:130%;">Vox = Vo Cos a = 20 m/s Cos 37° = <strong>15.97 m/s</strong></span> </p><p class="Estilo3" align="center"><span style="font-size:130%;">Voy = Vo Se n a = 20 m/s Sen 37° = <strong>12.03 m/s </strong></span></p><h3 class="Estilo3" align="center"><span style="font-size:130%;"><em>Paso 2 </em></span></h3><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Calcular el tiempo de altura máxima , donde Voy = 0 </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Por lo tanto : t = (Vfy - Voy) / g = (0 - 12.03 m/s) / 9.8 = <strong>1.22.seg. </strong></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;"><em><strong>Paso 3 </strong></em></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Calcular a) la altura máxima: </span></p><p style="font-weight: bold;" class="Estilo3" align="center"><span style="font-size:130%;"><span style="font-family:verdana;">Ymax = Voy t + gt^2 / 2= 12.03 m/s ( 1.22s) + (( -9.8m/s^2 )(1.22s)^2) / 2 = </span><strong><span style="font-family:verdana;">7.38m</span> </strong></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;"><em><strong>Paso 4 </strong></em></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Calcular b) el tiempo total . En este caso solo se multiplica el tiempo de altura máxima por 2, porque sabemos que la trayectoria en este caso es simétrica y tarda el doble de tiempo en caer el proyectil de lo que tarda en alcanzar la altura máxima. </span></p><p class="Estilo3" align="center"><span style="font-size:130%;"><span style="font-weight: bold;font-family:verdana;" >T total = tmax (2) = 1.22s (2) = </span><strong><span style="font-weight: bold;font-family:verdana;" >2.44</span> s. </strong></span></p><p class="Estilo3" align="center"><span style="font-size:130%;"><em><strong>Paso 5 </strong></em></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Calcular el alcance máximo, para lo cual usaremos esta formula: </span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">X = Vx t total = 15.97 m/s ( 2.44s) = <strong>38.96 m. </strong></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Paso 6 </span></p><p class="Estilo3" align="center"><span style="font-size:130%;"><span style="font-weight: bold;font-family:verdana;" >Vfy = gt + Voy = (- 9.8) ( 1seg.) + 12.03 m/s = </span><strong><span style="font-family:verdana;">2.23 m/s</span> </strong></span></p><p style="font-weight: bold;font-family:verdana;" class="Estilo3" align="center"><span style="font-size:130%;">Vfx = <strong>15.97</strong> m/s ,ya que esta es constante durante todo el movimiento.</span></p><p class="Estilo3" align="center"><span style="font-size:130%;">
<br /></span></p><p style="font-weight: bold;font-family:verdana;" align="justify"><span style="color: rgb(204, 0, 0);font-size:130%;" ><span>ejemplo 2-</span></span><span style="font-size:130%;"> Sea un proyetil lanzado desde un cañón. Si elegimos un sistema de referencia de modo que la dirección Y sea vertical y positiva hacia arriba, a <sub>y</sub> = - g y a <sub>x</sub> = 0. Además suponga que el instante t = 0, el proyectil deja de origen (X <sub>i </sub>= Y <sub>i</sub>V<sub>i</sub>. = 0) con una velocidad </span></p><p align="center"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht1.gif" width="514" height="254" /></span></p><p style="font-weight: bold;font-family:verdana;"><span style="font-size:130%;">Si Vi hace un ángulo qi con la horizontal, a partir de las definiciones de las funciones sen y cos se obtiene: </span></p><p align="center" style="font-family:verdana;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht2.gif" width="73" height="39" /></span></p><p align="center" style="font-family:verdana;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht3.gif" width="75" height="41" /></span></p><p align="center" style="font-family:verdana;"><span style="font-size:130%;">V<sub>xi</sub> = V<sub>i</sub> cos θ</span></p><p align="center" style="font-family:verdana;"><span style="font-size:130%;">Vyi = V<sub>i</sub> sen θ<sub>i</sub></span> </p><p style="font-weight: bold;font-family:verdana;" align="center"><span style="font-size:130%;">Como el movimiento de proyectiles es bi-dimencional, donde a<sub>x</sub> = 0 y a<sub>y</sub> = -g, o sea con aceleración constante, obtenemos las componentes de la velocidad y las coordenadas del proyectil en cualquier instante t, con ayuda de las ecuaciones ya utilizadas para el M.R.U.A. Expresando estas en función de las proyecciones tenemos:</span></p><p style="font-family:verdana;"><span style="font-size:130%;">X = V<sub>xi</sub>t = Vi cos θ<sub>i</sub> t </span></p><p style="font-family:verdana;"><span style="font-size:130%;">y = V<sub>yi</sub> t + ½ at<sup>2</sup></span> </p><p style="font-family:verdana;"><span style="font-size:130%;">V<sub>yf</sub> = V<sub>yi</sub> + at </span></p><p style="font-family:verdana;"><span style="font-size:130%;">2ay = V<sub>yf</sub><sup>2</sup> - V<sub>yi</sub><sup>2</sup></span></p><p style="font-weight: bold;font-family:verdana;" align="justify"><span style="font-size:130%;">Si un proyectil es lanzado horizontalmente desde cierta altura inicial, el movimiento es semi-parabólico.</span></p><span style="font-size:130%;"><!--[endif]--><o:p></o:p></span> <p style="margin: 6pt 0cm 0pt; text-align: justify; text-indent: 36pt;"><span lang="ES-AR" style="font-size:130%;"><o:p></o:p></span></p></blockquote>
<br /></div><p style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht4.gif" width="413" height="309" /></span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Las ecuaciones del movimiento considerando Vyi = 0 serían: </span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">X = V<sub>xi</sub> t </span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">y = y<sub>o</sub> - ½ gt<sup>2</sup></span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Recomendamos la realización de la práctica virtual <a href="http://rsta.pucmm.edu.do/profesor/nestorc/cinematica/parabolico/parabolico.htm">Movimiento bajo la aceleración constante de la gravedad</a>, donde se puede estudiar tanto el movimiento parabólico como el semi-parabólico.</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Combinando las ecuaciones arriba explicadas para el movimiento parabólico podemos algunas obtener ecuaciones útiles:</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">- Altura máxima que alcanza un proyectil: </span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht5.gif" width="129" height="42" /></span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">- Tiempo de vuelo del proyectil: </span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht6.gif" width="86" height="37" /></span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">- Alcance del proyectil : </span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"><img src="http://rsta.pucmm.edu.do/tutoriales/fisica/Leccion6/Images/6.1.ht7.gif" width="276" height="41" /></span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Atendiendo a esta última ecuación, invitamos al lector a demostrar que para una velocidad dada el máximo alcance se logra con una inclinacion de 45o respecto a la horizontal.</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"><strong>EJEMPLO</strong> TIRO PARABÓLICO:</span> </p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Calcular la distancia, la altura y el tiempo de caída de un tiro parabólico que lleva una velocidad de 30m/s y forma una ángulo de 60° con la horizontal.
<br />
<br />Primero calculamos la distancia recorrida.</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">d= v<sub>1</sub><sup>2</sup>sen2a / g = (30m/s)<sup>2</sup> sen 2(60°) / 9.8 m/s<sup>2</sup> = 158.99 m
<br />
<br />Ahora la altura alcanzada.</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">h= v<sup>2</sup><sub>1</sub>sen<sup>2</sup>a / 2g= (30 m/s)<sup>2</sup> sen<sup>2</sup> (60°) / 2(9.8 m/s<sup>2</sup>) = 36.29 m</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Por último el tiempo realizado.</span></p><p style="color: rgb(0, 0, 0); text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">t= v<sub>1</sub> sen a / g= 30 m/s (sen 60°) / 9.8 m/s<sup>2</sup> = 2.85 s</span></p><p style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;"><span style="font-size:130%;"><object codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" width="550" height="550"><param name="_cx" value="14552"><param name="_cy" value="14552"><param name="FlashVars" value="14552"><param name="Movie" value="Cannon_04.swf"><param name="Src" value="Cannon_04.swf"><param name="WMode" value="Window"><param name="Play" value="-1"><param name="Loop" value="-1"><param name="Quality" value="High"><param name="SAlign" value=""><param name="Menu" value="-1"><param name="Base" value=""><param name="AllowScriptAccess" value="always"><param name="Scale" value="ShowAll"><param name="DeviceFont" value="0"><param name="EmbedMovie" value="0"><param name="BGColor" value=""><param name="SWRemote" value="">
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<br /></div><p style="line-height: normal; font-weight: bold; color: rgb(0, 0, 0); text-align: justify;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><span style="color: rgb(204, 0, 0);">TAREA</span>:<o:p></o:p></span></p><p style="line-height: normal; font-weight: bold; color: rgb(0, 0, 0); font-style: italic; text-align: justify;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">I<span style="font-weight: bold; font-style: italic;font-family:verdana;" >NSTRUCCIONES</span></span><span style="font-weight: bold; font-style: italic;font-family:verdana;font-size:130%;" ><o:p></o:p>: Resolver los siguientes ejercicios con ayuda de su maestro de ciencia fisica.<o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">1.- Un proyectil es disparado con una rapidez inicial de 75.2 mIs, a un ángulo de 34.5° por encima de la horizontal a lo largo de un campo de tiro plano. Calcule <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">a) La máxima altura alcanzada por el proyectil. <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">b) El tiempo que total que el proyectil permanece en el aire <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">c) La distancia horizontal total <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">d) La velocidad de X y Y del proyectil después de 1.5 s de haber sido disparado <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">
<br /></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">2.- Una flecha se dispara con un ángulo de 50° con respecto a la horizontal y con una velocidad de 35 m/s. <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">a) ¿Cuál es su posición horizontal y vertical después de 4 segundos? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">b) Determine las componentes de su velocidad después de 4 segundos. <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">c) ¿Cuál es la velocidad en X y Y después de 4 segundos? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">
<br /></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">3- Una piedra se arroja horizontalmente a 15 m/s desde la parte más alta de un risco de 44 m de altura. </span><span style="font-size:130%;"><o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">a) ¿Qué tiempo tarda la piedra en llegar a la base del risco? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">b) ¿Qué tan lejos de la base del risco choca la piedra con el piso? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">c) ¿Cuál su velocidad horizontal después de 1.5 seg<span style="color: rgb(0, 0, 0);">undos? </span><o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">
<br /></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">4- Una pelota de golf se golpea con un ángulo de 45° con la horizontal. Si la velocidad inicial de la pelota es de 50 m/s: <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">a) ¿Cuánto tiempo permanece la pelota en el aire? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">b) ¿Cuál su altura máxima? <o:p></o:p></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;">c) ¿Cuál su alcance horizontal?
<br /></span></p><p style="line-height: normal; color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:verdana;" class="MsoNormal"><span style="font-size:130%;">
<br /></span></p><div style="text-align: justify; font-style: italic; font-weight: bold;font-family:verdana;"><!--comienzo_cuerpo--></div><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">5- Se lanza un proyectil con una velocidad inicial de 200 m/s y una inclinación, sobre la horizontal, de 30°. Suponiendo despreciable la pérdida de velocidad con el aire, calcular:</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">a) ¿Cuál es la altura máxima que alcanza la bala?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">b) ¿A qué distancia del lanzamiento alcanza la altura máxima?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">c) ¿A qué distancia del lanzamiento cae el proyectil?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: a) 39,36 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> b) 1732,05 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> c) 3464,1 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">
<br /></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">6-Se dispone de un cañón que forma un ángulo de 60° con la horizontal. El objetivo se encuentra en lo alto de una torre de 26 m de altura y a 200 m del cañón. Determinar:</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">a) ¿Con qué velocidad debe salir el proyectil?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">b) Con la misma velocidad inicial ¿desde que otra posición se podría haber disparado?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: a) 49,46 m/s</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> b) 17 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">
<br /></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">7- Un chico patea una pelota contra un arco con una velocidad inicial de 13 m/s y con un ángulo de 45° respecto del campo, el arco se encuentra a 13 m. Determinar:</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">a) ¿Qué tiempo transcurre desde que patea hasta que la pelota llega al arco?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">b) ¿Convierte el gol?, ¿por qué?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">c) ¿A qué distancia del arco picaría por primera vez?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: a) 1,41 s</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> b) No</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> c) 17,18 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">
<br /></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">8- Sobre un plano inclinado que tiene un ángulo α = 30°, se dispara un proyectil con una velocidad inicial de 50 m/s y formando un ángulo β = 60° con la horizontal. Calcular en que punto del plano inclinado pegará.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: 165,99 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">
<br /></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">9- Un cañón que forma un ángulo de 45° con la horizontal, lanza un proyectil a 20 m/s, a 20 m de este se encuentra un muro de 21 m de altura. Determinar:</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">a) ¿A qué altura del muro hace impacto el proyectil?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">b) ¿Qué altura máxima logrará el proyectil?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">c) ¿Qué alcance tendrá?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">d) ¿Cuánto tiempo transcurrirá entre el disparo y el impacto en el muro?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: a) 9,75 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> b) 10,2 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> c) 40,82 m</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;"> d) 1,41 s</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">
<br /></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">10- Un mortero dispara sus proyectiles con una velocidad inicial de 800 km/h, ¿qué inclinación debe tener el mortero para que alcance un objetivo ubicado a 4000 m de este?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Respuesta: 26° 16´ 16"</span></p><div face="verdana" style="text-align: justify; font-style: italic; font-weight: bold;"><span style="font-size:130%;">
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<br /></span><span style="font-size:130%;"><o:p></o:p></span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;" class="MsoNormal"><span style="font-size:130%;"><o:p></o:p></span></p><div style="text-align: justify; font-style: italic; font-family: verdana; font-weight: bold;"><span style="font-size:130%;">
<br /></span></div><h2 style="color: rgb(0, 0, 0); text-align: center; font-style: italic; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">Responder el siguiente cuestionario:</span></h2><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">1)En el tiro parabólico ¿qué tipo de movimiento se manifiesta en el eje "x"?.</span></p><p style="color: rgb(0, 0, 0); font-style: italic; text-align: justify; font-weight: bold;font-family:georgia;"><span style="font-size:130%;">2)En el tiro parabólico ¿qué tipo de movimiento se manifiesta en el eje "y"?.</span></p><div style="text-align: justify;"><span style="color: rgb(0, 0, 0); font-weight: bold;font-family:verdana;font-size:130%;" ><span style="color: rgb(0, 0, 0);">3)En qué posición es nula la velocidad en el eje "y"?</span></span>
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<br /></span><embed style="color: rgb(0, 0, 0);" type="application/x-shockwave-flash" src="http://www.youtube.com/v/dKovgwKYaj4&hl=" fs="1&color1=" color2="0x4e9e00&border=" allowscriptaccess="always" allowfullscreen="true" width="445" height="364"></embed><span style="font-size:130%;">
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<br /></span><embed type="application/x-shockwave-flash" src="http://www.youtube.com/v/W0DkKJx5f6A&hl=" allowfullscreen="true" allowscriptaccess="always" color2="0x9461ca&border=" fs="1&color1=" width="445" height="364"></embed> </p><p style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;"><span style="font-size:130%;">algunos enlaces:</span></p><p style="font-weight: bold; color: rgb(0, 0, 0); font-style: italic;font-family:georgia;"><span style="font-size:130%;"><a href="http://descartes.cnice.mec.es/materiales_didacticos/comp_movimientos/parabolico.htm">http://descartes.cnice.mec.es/materiales_didacticos/comp_movimientos/parabolico.htm</a></span></p><p style="font-weight: bold; font-style: italic;font-family:verdana;"><span style="font-size:130%;"><a href="http://descartes.cnice.mec.es/materiales_didacticos/comp_movimientos/parabolico.htm">http://www.sc.ehu.es/sbweb/fisica/cinematica/parabolico/parabolico.htm</a></span></p><p style="font-weight: bold; font-style: italic;font-family:verdana;"><span style="font-size:130%;"><a href="http://descartes.cnice.mec.es/materiales_didacticos/comp_movimientos/parabolico.htm">http://www.monografias.com/trabajos-pdf/movimiento-dos-dimensiones/movimiento-dos-dimensiones.pdf</a></span></p><p><span style="font-size:130%;"><a href="http://descartes.cnice.mec.es/materiales_didacticos/comp_movimientos/parabolico.htm">
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style="line-height: normal;"><span style="font-size: 12pt; font-family: "Arial","sans-serif";">Se denomina movimiento parabólico al realizado por un objeto cuya trayectoria describe una <a href="http://es.wikipedia.org/wiki/Par%C3%A1bola_%28matem%C3%A1tica%29" title="Parábola (matemática)"><span style="color: windowtext; text-decoration: none;">parábola</span></a>. Se corresponde con la trayectoria ideal de un <a href="http://es.wikipedia.org/wiki/Proyectil" title="Proyectil"><span style="color: windowtext; text-decoration: none;">proyectil</span></a> que se mueve en un medio que no ofrece resistencia al avance y que está sujeto a un <a href="http://es.wikipedia.org/wiki/Campo_gravitatorio" title="Campo gravitatorio"><span style="color: windowtext; text-decoration: none;">campo gravitatorio</span></a> uniforme.<o:p></o:p></span></p> <p class="MsoNormal"><span style="font-size: 12pt; line-height: 115%; font-family: "Arial","sans-serif";">Puede ser analizado como la composición de dos movimientos rectilíneos: un </span><span style="font-size: 12pt; line-height: 115%; font-family: "Times New Roman","serif";"><a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniforme" title="Movimiento rectilíneo uniforme"><span style="font-family: "Arial","sans-serif"; color: windowtext; text-decoration: none;">movimiento rectilíneo uniforme</span></a></span><span style="font-size: 12pt; line-height: 115%; font-family: "Arial","sans-serif";"> horizontal y un </span><span style="font-size: 12pt; line-height: 115%; font-family: "Times New Roman","serif";"><a href="http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniformemente_acelerado" title="Movimiento rectilíneo uniformemente acelerado"><span style="font-family: "Arial","sans-serif"; color: windowtext; text-decoration: none;">movimiento rectilíneo uniformemente acelerado</span></a></span><span style="font-size: 12pt; line-height: 115%; font-family: "Arial","sans-serif";"> vertical</span></p><p class="MsoNormal"><span style="font-size: 12pt; line-height: 115%; font-family: "Arial","sans-serif";"><br /></span></p> <p></p><font size="3"><span style="font-family: arial; color: rgb(0, 0, 0);"></span></font><font size="3"><span style="font-family: arial; color: rgb(0, 0, 0);"></span></font>krissia Urrutiahttp://www.blogger.com/profile/04518663748184719067noreply@blogger.com2