document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=652685>Question 652685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by the quadratic equation<BR>\n" );
document.write( "h = -16t2 +30t +4\r<BR>\n" );
document.write( "\n" );
document.write( "a)	How long does it take the ball to reach a height of 18ft?<BR>\n" );
document.write( "b)	How long does it take the ball to hit the ground?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408077 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by the quadratic equation<BR>\n" );
document.write( "h = -16t2 +30t +4\r<BR>\n" );
document.write( "\n" );
document.write( "a)	How long does it take the ball to reach a height of 18ft?<BR>\n" );
document.write( "set h to 18 and solve for t:<BR>\n" );
document.write( "h = -16t^2 +30t +4<BR>\n" );
document.write( "18 = -16t^2 +30t +4<BR>\n" );
document.write( "0 = -16t^2 +30t - 14<BR>\n" );
document.write( "0 = 16t^2 -30t + 14<BR>\n" );
document.write( "0 = 8t^2 -15t + 7<BR>\n" );
document.write( "0 = 8t^2 -8t -7t + 7<BR>\n" );
document.write( "0 = (8t^2 -8t) - (7t - 7)<BR>\n" );
document.write( "0 = 8t(t-1) - 7(t-1)<BR>\n" );
document.write( "0 = (t-1)(8t-7)<BR>\n" );
document.write( "t = {1, 7/8}<BR>\n" );
document.write( "t = {1, 0.875}<BR>\n" );
document.write( "it reaches 18 ft twice.  Once at 0.875 sec (going up) and again at 1 sec (going down).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)	How long does it take the ball to hit the ground?<BR>\n" );
document.write( "set h to 0 and solve for t:<BR>\n" );
document.write( "h = -16t^2 +30t +4<BR>\n" );
document.write( "0 = -16t^2 +30t +4<BR>\n" );
document.write( "0 = 16t^2 -30t -4<BR>\n" );
document.write( "0 = 8t^2 -15t -2<BR>\n" );
document.write( "0 = 8t^2 -16t+t -2<BR>\n" );
document.write( "0 = (8t^2-16t) + (t-2)<BR>\n" );
document.write( "0 = 8t(t-2) + (t-2)<BR>\n" );
document.write( "0 = (t-2)(8t+1)<BR>\n" );
document.write( "t = {-1/8, 2}<BR>\n" );
document.write( "we can throw out the negative solution leaving:<BR>\n" );
document.write( "t = 2 seconds\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );