document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074061>Question 1074061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear... <BR>\n" );
document.write( "Can someone help me with this?\r<BR>\n" );
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document.write( "A projectile is fired straight upward from ground level with an initial velocity of 80 feet per second. <BR>\n" );
document.write( "During which interval of time will the projectile's height  exceed 96 feet? \r<BR>\n" );
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document.write( "I do not know how to use the position formula here. <BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688779 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the problem uses feet, so we will use 16 feet per second per second which is derived from the force of gravity<BR>\n" );
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document.write( "the formula for height at a give time is<BR>\n" );
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document.write( "h(t) = -16t^2 + v(0)t + h(0)<BR>\n" );
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document.write( "Note that h(0) is 0 at ground level<BR>\n" );
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document.write( "the graph of h(t) is a parabola that open downward<BR>\n" );
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document.write( "we are given v(0) = 80 feet per second<BR>\n" );
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document.write( "h(t) = -16t^2 +80t<BR>\n" );
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document.write( "we want to find the vertex of the parabola by taking the first derivative of h(t) and setting it = 0 and solve for t<BR>\n" );
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document.write( "h'(t) = -32t + 80<BR>\n" );
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document.write( "-32t = -80<BR>\n" );
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document.write( "t = 2.5 seconds<BR>\n" );
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document.write( "this tells us that the maximum height of the projectile occurs at 2.5 seconds after launch<BR>\n" );
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document.write( "h(t) = -16(2.5)^2 + 80(2.5) = 100 feet<BR>\n" );
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document.write( "The maximum height is 100 feet at 2.5 seconds after launch<BR>\n" );
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document.write( "now we look for the time after launch when the projectile reaches 96 feet<BR>\n" );
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document.write( "96 = -16t^2 + 80t<BR>\n" );
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document.write( "16t^2 -80t +96 = 0 <BR>\n" );
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document.write( "divide both sides of = by 16<BR>\n" );
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document.write( "t^2 -5t +6 = 0<BR>\n" );
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document.write( "factor the quadratic<BR>\n" );
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document.write( "(t-3) ^ (t-2) = 0<BR>\n" );
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document.write( "t is 3 or 2<BR>\n" );
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document.write( "Note the max height occurs at 2.5 seconds<BR>\n" );
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document.write( "The projectile's height exceeds 96 feet during the time interval (2, 3)<BR>\n" );
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document.write( "here is the graph of the projectiles path<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+5%2C+-1%2C+100%2C+-16x%5E2+%2B80x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+5%2C+-1%2C+100%2C+-16x%5E2+%2B80x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( ":\r<BR>\n" );
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