document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620999>Question 620999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You launch a rocket into the air with an initial upward velocity of 60ft/sec. starting at a height of 3ft.\r<BR>\n" );
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document.write( "How long until it hits the ground?<BR>\n" );
document.write( "what was the maximum height of the rocket?<BR>\n" );
document.write( "after how long did the maximum height occur?<BR>\n" );
document.write( "at what two times was the rocket 50ft in the air?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390502 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=390502\">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( "The height of a projectile at time <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> is given by the function\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\"> is the acceleration due to gravity near the surface of whatever planet you are on.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 32\ \text{\frac{ft}{sec^2}}\"> if you are still on Earth.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE v_o\"> is the initial upward velocity in feet per second, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h_o\"> is the initial height in feet.\r<BR>\n" );
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document.write( "The ground is height zero.  Set the function equal to zero and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\">.  Use the quadratic formula.  Discard the negative root.\r<BR>\n" );
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document.write( "Since acceleration due to gravity is a negative quantity with respect to the initial direction of the rocket, the graph of the function is a parabola opening downward.  Hence the vertex of the parabola is at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(t_v,h(t_v)\right)\">, where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t_v\"> represents the time that the vertex is obtained and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h(t_v)\"> is the maximum height obtained.  Recall that the vertex of the parabola <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \rho(x)\ =\ ax^2\ +\ bx\ +\ c\"> has an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">-coordinate of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "Set the function equal to 50 and solve the quadratic for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\">.  Use the quadratic formula.\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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