document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909476>Question 909476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need someone who is good in physics i need help please .i do not understand this question.\r<BR>\n" );
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document.write( "An athlete executing a long jump leaves the ground at 28.0 angle and travels 7.80 m a)What was the take off speed? b)If this speed were increased by just 5.0%,how much longer would the jump be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551934 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The athlete left the ground with an initial velocity of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in m/s), making an angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%5Eo ALIGN=MIDDLE  ALT=\"28%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the ground. The magnitude and direction of the athlete's velocity changed over time under the influence of the acceleration of gravity, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=9.6 ALIGN=MIDDLE  ALT=\"g=9.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Fs%5E2 ALIGN=MIDDLE  ALT=\"m%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > downwards, until the athlete landed on the ground , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds after leaving the ground.<BR>\n" );
document.write( "The velocity can be decomposed into a horizontal component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29 ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and a vertical component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Asin%2828%5Eo%29 ALIGN=MIDDLE  ALT=\"v%2Asin%2828%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "FOR THE HORIZONTAL COMPONENT OF THE MOTION:<BR>\n" );
document.write( "We assume that the athlete is jumping over a perfectly horizontal surface, and that air resistance does not really affect him/her at the speeds he/she is capable of attaining.<BR>\n" );
document.write( "That makes his horizontal speed constant at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29 ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds the athlete is airborne.<BR>\n" );
document.write( "As a consequence of our assumptions, we know that<BR>\n" );
document.write( "the athlete's initial horizontal velocity (in m/s)<BR>\n" );
document.write( "times the time in the air (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > , in seconds)<BR>\n" );
document.write( "equals the horizontal displacement, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > in meters (7.8 m, in this case).<BR>\n" );
document.write( "So, in general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29%2At=d ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29%2At=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and in this particular case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29%2At=7.8 ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29%2At=7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > . <BR>\n" );
document.write( " <BR>\n" );
document.write( "FOR THE VERTICAL COMPONENT OF THE MOTION:<BR>\n" );
document.write( "The vertical component of the velocity changes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Asin%2828%5Eo%29 ALIGN=MIDDLE  ALT=\"v%2Asin%2828%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to zero over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F2 ALIGN=MIDDLE  ALT=\"t%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds, at a constant rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=9.8 ALIGN=MIDDLE  ALT=\"g=9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Fs%5E2 ALIGN=MIDDLE  ALT=\"m%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Asin%2828%5Eo%29%2F%28t%2F2%29=9.8 ALIGN=MIDDLE  ALT=\"v%2Asin%2828%5Eo%29%2F%28t%2F2%29=9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Asin%2828%5Eo%29=9.8%2A%28t%2F2%29 ALIGN=MIDDLE  ALT=\"v%2Asin%2828%5Eo%29=9.8%2A%28t%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Asin%2828%5Eo%29=4.9t%29 ALIGN=MIDDLE  ALT=\"v%2Asin%2828%5Eo%29=4.9t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=v%2Asin%2828%5Eo%29%2F4.9%29 ALIGN=MIDDLE  ALT=\"t=v%2Asin%2828%5Eo%29%2F4.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "PUTTING IT ALL TOGETHER:<BR>\n" );
document.write( "How are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > related?<BR>\n" );
document.write( "Putting together <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29%2At=d ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29%2At=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=v%2Asin%2828%5Eo%29%2F4.9%29 ALIGN=MIDDLE  ALT=\"t=v%2Asin%2828%5Eo%29%2F4.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Acos%2828%5Eo%29%2A%28v%2Asin%2828%5Eo%29%2F4.9%29=d ALIGN=MIDDLE  ALT=\"v%2Acos%2828%5Eo%29%2A%28v%2Asin%2828%5Eo%29%2F4.9%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28cos%2828%5Eo%29%2Asin%2828%5Eo%29%2F4.9%29%2Av%5E2 ALIGN=MIDDLE  ALT=\"d=%28cos%2828%5Eo%29%2Asin%2828%5Eo%29%2F4.9%29%2Av%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting the approximate values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2828%5Eo%29=0.46947 ALIGN=MIDDLE  ALT=\"sin%2828%5Eo%29=0.46947\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2828%5Eo%29=0.88295 ALIGN=MIDDLE  ALT=\"cos%2828%5Eo%29=0.88295\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "to get the approximate formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0.08460v%5E2 ALIGN=MIDDLE  ALT=\"d=0.08460v%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "WHAT DOES THAT TELL YOU?:<BR>\n" );
document.write( "a) At this point you can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0.08460v%5E2 ALIGN=MIDDLE  ALT=\"d=0.08460v%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.8=0.08460v%5E2 ALIGN=MIDDLE  ALT=\"7.8=0.08460v%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5E2=7.8%2F0.08460 ALIGN=MIDDLE  ALT=\"v%5E2=7.8%2F0.08460\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5E2=92.20 ALIGN=MIDDLE  ALT=\"v%5E2=92.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=sqrt%2892.20%29 ALIGN=MIDDLE  ALT=\"v=sqrt%2892.20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=9.6 ALIGN=MIDDLE  ALT=\"v=9.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "So, the initial velocity was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289.6%29 ALIGN=MIDDLE  ALT=\"highlight%289.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/s.<BR>\n" );
document.write( " <BR>\n" );
document.write( "b) If an athlete jumps at the same angle, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the initial velocity, he/she will get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2=4 ALIGN=MIDDLE  ALT=\"2%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > times as far.<BR>\n" );
document.write( "If the athlete jumps with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.05 ALIGN=MIDDLE  ALT=\"1.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > times (5% more) initial velocity,<BR>\n" );
document.write( "he/she will get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.05%5E2=1.1025 ALIGN=MIDDLE  ALT=\"1.05%5E2=1.1025\"   DISABLED_style= \"max-width:90%; height:auto;\" > times farther.<BR>\n" );
document.write( "That would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.1025%2A7.8=8.6 ALIGN=MIDDLE  ALT=\"1.1025%2A7.8=8.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "So, jumping with 5% higher initial velocity, the athlete will travel 8.7 meters.<BR>\n" );
document.write( "That means that his/her jump would be<BR>\n" );
document.write( "8.6 m - 7.8 m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.8%29 ALIGN=MIDDLE  ALT=\"highlight%280.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > m longer,<BR>\n" );
document.write( "or 1.10 times longer (10% longer). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );