document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181576>Question 181576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a soldier in basic training fores a rocket propelled grenade straight up from the ground level with an initial velocity of 256 ft/sec, then its height above the ground at time t seconds is given by the function h(t) = -16t^2 + 256t.\r<BR>\n" );
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document.write( "A. what is the maximum height reached by the grenade?<BR>\n" );
document.write( "B. How long does it take for the grenade to reach the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136169 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a soldier in basic training fores a rocket propelled grenade straight up from the ground level with an initial velocity of 256 ft/sec, then its height above the ground at time t seconds is given by the function h(t) = -16t^2 + 256t. <BR>\n" );
document.write( "A. what is the maximum height reached by the grenade?<BR>\n" );
document.write( "B. How long does it take for the grenade to reach the ground?<BR>\n" );
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document.write( "1st of all, an RPG has a rocket motor, it will accelerate straight up.  RP means Rocket Propelled.  <BR>\n" );
document.write( "This problem would apply to a short range mortar, or, with the numbers given, a hand grenade.<BR>\n" );
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document.write( "Anyway,<BR>\n" );
document.write( "For max height, find where the time when the upward speed is zero, which is where it stops going up and starts going down.<BR>\n" );
document.write( "To do that, set the 1st derivative to zero.<BR>\n" );
document.write( "-32t + 256 = 0<BR>\n" );
document.write( "t = 8 seconds.<BR>\n" );
document.write( "At t=8, the height is 256*8 - 16*64<BR>\n" );
document.write( "A. hmax = 1024 feet (optimistic for a hand grenade)<BR>\n" );
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document.write( "B. It takes the same time to fall as it does to reach max height, so that's 16 seconds.<BR>\n" );
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