document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723515>Question 723515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground (in feet) t seconds after the arrow is released. (If air resistance is neglected, a quadratic model provides a good approximation for the flight of a projectile.)<BR>\n" );
document.write( "(A) Find d(t)<BR>\n" );
document.write( "(B) At what times (to two decimal places) will the arrow be 250 feet above the ground?<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 #443242 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground (in feet) t seconds after the arrow is released. (If air resistance is neglected, a quadratic model provides a good approximation for the flight of a projectile.)<BR>\n" );
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document.write( "(A) Find d(t)<BR>\n" );
document.write( "Find the initial velocity (v) of the arrow using the form -16t^2 + vt = d(t)<BR>\n" );
document.write( "t=4.5, d(t)= 324<BR>\n" );
document.write( "-16(4.5^2) + 4.5v = 324<BR>\n" );
document.write( "-16(20.25) + 4.5v = 324<BR>\n" );
document.write( "-324 + 4.5v = 324<BR>\n" );
document.write( "4.5v = 324 + 324<BR>\n" );
document.write( "4.5v = 648<BR>\n" );
document.write( "v = 648/4.5<BR>\n" );
document.write( "v = 144 ft/sec is the initial upward velocity of the arrow<BR>\n" );
document.write( "the equation<BR>\n" );
document.write( "d(t) = -16t^2 + 144t<BR>\n" );
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document.write( "(B) At what times (to two decimal places) will the arrow be 250 feet above the ground?<BR>\n" );
document.write( "-16t^2 + 144t = 250<BR>\n" );
document.write( "-16t^2 + 144t - 250 = 0<BR>\n" );
document.write( "Solve for t using the quadratic formula, <BR>\n" );
document.write( "I got t = 2.35 and 6.65 sec at 250 ft<BR>\n" );
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document.write( "Graphically, green line is 250 ft, blue line is 324 ft<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+15%2C+-100%2C+400%2C+-16x%5E2%2B144x%2C+250%2C+324%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+15%2C+-100%2C+400%2C+-16x%5E2%2B144x%2C+250%2C+324%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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