document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970087>Question 970087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second. The height, h is given by the equation h(t)=-16t^2+128t (without any air resistance)\r<BR>\n" );
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document.write( "How long will it take for the rocket to reach its maximum height?\r<BR>\n" );
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document.write( "What is the maximum height of the rocket?\r<BR>\n" );
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document.write( "How long will it take for the rocket to return to the ground?\r<BR>\n" );
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document.write( "After how many seconds will the rocket be 112 feet above the ground?\r<BR>\n" );
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document.write( "Why is the equation including h(t)= rather then y=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592753 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  h(t)=-16t^2+128t\r<BR>\n" );
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document.write( "maximum height occurs at the vertex.<BR>\n" );
document.write( "t value at vertex is -b/2a<BR>\n" );
document.write( "b=128<BR>\n" );
document.write( "a=-16\r<BR>\n" );
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document.write( "vertex has t value of -128/-32   = 4 seconds to reach maximum height\r<BR>\n" );
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document.write( "h(4)=-16 (4^2) + (128) (4)<BR>\n" );
document.write( "h=-256+512=256feet\r<BR>\n" );
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document.write( "4 seconds to return to ground, because launched from ground, and parabolas are symmetric.\r<BR>\n" );
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document.write( "112=-16(t^2) +128<BR>\n" );
document.write( "Divide everything by 16<BR>\n" );
document.write( "7=-1 (t^2) +8<BR>\n" );
document.write( "-1=-1 (t^2)<BR>\n" );
document.write( "1=1 t^2<BR>\n" );
document.write( "t^2=1<BR>\n" );
document.write( "t=(1) second OR 7 seconds, on the way down.  Note, t=-1 is a mathematical but not real world solution.\r<BR>\n" );
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document.write( "It is h(t), because height is a function of t.  That is by convention.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-1%2C8%2C0%2C400%2C-16x%5E2%2B128x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-1%2C8%2C0%2C400%2C-16x%5E2%2B128x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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