document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485107>Question 485107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a long distance runner has an average speed of 5 m/s during a race. how far does the runner travel in 25 minutes? express the answer in m, km, and miles. \r<BR>\n" );
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document.write( "and lastly, \r<BR>\n" );
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document.write( "A rock is dropped off the side of a bridge and hits the water below at 2.5 s later. what is the rocks velocity when it hits the water, the average velocity as it fell and the height of the bridge above the water.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331833 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Your second problem:\r<BR>\n" );
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document.write( "You need to choose the measurement system you want to use.  Acceleration due to gravity in kms is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\ =\ -9.8 m/sec^2\">, whereas in fps it is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\ =\ -32 ft/sec^2\">.  The values are negative because of the convention that up is positive.\r<BR>\n" );
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document.write( "I'm just going to do the problem using <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\"> and then you can substitute the appropriate acceleration value and do the arithmetic.\r<BR>\n" );
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document.write( "The instantaneous velocity of a falling body is the integral of acceleration with respect to time plus a constant which is the initial velocity, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\">\r<BR>\n" );
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document.write( "Since the rock was dropped we can presume that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ v(t)\ =\ \int\,g\ dt\ =\ gt\ +\ v_o\">\r<BR>\n" );
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document.write( "Which is to say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ v(t)\ =\ gt\">\r<BR>\n" );
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document.write( "Substitute 2.5 seconds for the time because that is what is given and multiply by the appropriate value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\">.  If you use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -9.8\"> your answer will be in meters per second, but if you use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -32\"> then your answer will be in feet per second.\r<BR>\n" );
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document.write( "The height is determined by integrating velocity as a function of time.  Very conveniently the function we just evaluated to find the final velocity.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,gt\ +\ v_o\,dt\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ C\">\r<BR>\n" );
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document.write( "Where the constant of integration is the initial height, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\">\r<BR>\n" );
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document.write( "For simplicity's sake, we will take the initial height to be zero and then consider the surface of the water to be some negative height.\r<BR>\n" );
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document.write( "Again, we substitute 0 for the initial values and get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -\frac{1}{2}gt^2\">\r<BR>\n" );
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document.write( "And again, substitute 2.5 for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> and your chosen value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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