document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234663>Question 234663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you throw a rock straight up with an initial velocity of 20 m/s, <BR>\n" );
document.write( "a) How high does it travel? <BR>\n" );
document.write( "b) How long does it take for the rock to reach its maximum height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173028 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=173028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The vertical distance as a function of time is given by:\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\ +\ v_ot\ +\ h_o\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g = 9.8\"> m/secē is the acceleration due to gravity, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\ = 20\"> m/sec is the initial velocity, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\"> is the height of your hand above the ground when you let go of the rock.\r<BR>\n" );
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document.write( "First answer part b).  To answer part b), realize that the graph of this function is a parabola opening downward with vertex at\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(t_{max},\,h(t_{max})\right)\">\r<BR>\n" );
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document.write( "and that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t_m\ =\ \frac{-v_o}{2\,\cdot\,\frac{g}{2}}\ =\ -\frac{v_o}{g}\">\r<BR>\n" );
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document.write( "because for a general quadratic function, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ =\ ax^2\ +\ bx\ +\ c\">, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "Once you have calculated <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t_{max}\">, which is the solution to part b), find the value of the height function for that time, that is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t_{max})\ =\ -\frac{1}{2}g(t_{max})^2\ +\ v_ot_{max}\ +\ h_o\">\r<BR>\n" );
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document.write( "Making the appropriate substitution for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\"> based on your personal physical stature and the mechanics of your throwing arm and you will have the solution to part a) \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" );
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