document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167804>Question 1167804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Robin Hood shoots an arrow from a window in Nottingham Castle to escape the evil Prince John.  The relation h = -t2 + 4t + 21 models the height of the arrow as it makes its way to a 9 m high tree across the moat. t is time in seconds, h is height in metres.\r<BR>\n" );
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document.write( " How high is the window?\r<BR>\n" );
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document.write( "What is the maximum height of the arrow?\r<BR>\n" );
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document.write( " If the arrow hits the top of the tree on its way down, how long does it take the arrow to reach the tree?<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 #792398 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=792398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h=-t^2+4t+21\r<BR>\n" );
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document.write( "The window is 21 m high (the constant in the formula)\r<BR>\n" );
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document.write( "the maximum is at t=-b/2a or -4/-2 or at 2 seconds<BR>\n" );
document.write( "h(2)=-4+8+21=25 m maximum\r<BR>\n" );
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document.write( "9=-t^2+4t+21<BR>\n" );
document.write( "t^2-4t-12=0<BR>\n" );
document.write( "(t-6)(t+2)=0<BR>\n" );
document.write( "t=6 and -2, which can be ignored.<BR>\n" );
document.write( "at 6 seconds, h will be 9 meters, so the answer is 6 seconds\r<BR>\n" );
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