document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133135>Question 133135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height h (in feet) above the ground of a baseball depends upon the time t (in seconds) it has been in flight. Cameron takes a mighty swing, but hits a bloop sinlge whose height is described approximately by the equation h=80t-16t^2. Ho long is the ball in the air? The ball reaches its maximum heght after how many seconds of light? What is the maximum height? How much time does it take for the ball to reach a hieght of 60 feet? On its way back down, the ball is again 60 feet above the ground; what is the value of t when this happens? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97368 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> height is described approximately by the equation h=80t-16t^2.<BR>\n" );
document.write( "How long is the ball in the air?<BR>\n" );
document.write( "Height = zero when the ball is back on the ground:<BR>\n" );
document.write( "-16t^2+80t = 0<BR>\n" );
document.write( "-16t(t-5) = 0<BR>\n" );
document.write( "t = 0 sec or t = 5 sec.<BR>\n" );
document.write( "The ball is in the air 5 seconds.<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "The ball reaches its maximum height after how many seconds of flight? <BR>\n" );
document.write( "What is the maximum height? <BR>\n" );
document.write( "max = -b/2a = -80/(-32) = 5/2 seconds<BR>\n" );
document.write( "max height is h(5/2) = 80(5/2)-16(5/2)^2 = 200 -100 = 100 ft.<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "How much time does it take for the ball to reach a height of 60 feet?<BR>\n" );
document.write( "-16t^2+80t = 60<BR>\n" );
document.write( "Divide thru by -4 to get:<BR>\n" );
document.write( "4t^2-20t+15 = 0<BR>\n" );
document.write( "t = [20 +- sqrt(400-4*4*15)]/8<BR>\n" );
document.write( "t = [20 +- sqrt(160)]/8<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( " or t = [20-4sqrt(10)]/8<BR>\n" );
document.write( "t = 0.918861 seconds<BR>\n" );
document.write( "------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "On its way back down, the ball is again 60 feet above the ground; what is the value of t when this happens?<BR>\n" );
document.write( "t = [20 + 4sqrt(10)]/8<BR>\n" );
document.write( "t = 4.0811 seconds<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );