document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95079>Question 95079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a ball is thrown upward from the roof of a building 80 m tall with an initial velocity of 15 m/s, its approximate height h after t is given by <BR>\n" );
document.write( "h = -5t^2 + 15t + 80.<BR>\n" );
document.write( "When we used feet, the t^2-coefficient was -16 (from the fact that the acceleration due to gravity is approximately 32 ft/s^2). When we use meters as the height, the t^2-coefficient is -5 (that same accelerations becomes approximately 10 m/s^2). Use this information to solve 31 and 32.\r<BR>\n" );
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document.write( "31)Science and Medicine: When will the ball reach a height of 85 m?\r<BR>\n" );
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document.write( "32)Science and Medicine: How long does it take the ball to fall back to the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69167 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=69167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a ball is thrown upward from the roof of a building 80 m tall with an initial velocity of 15 m/s, its approximate height h after t is given by <BR>\n" );
document.write( "h(t) = -5t^2 + 15t + 80.<BR>\n" );
document.write( "When we used feet, the t^2-coefficient was -16 (from the fact that the acceleration due to gravity is approximately 32 ft/s^2). When we use meters as the height, the t^2-coefficient is -5 (that same accelerations becomes approximately 10 m/s^2). Use this information to solve 31 and 32.\r<BR>\n" );
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document.write( "31)Science and Medicine: When will the ball reach a height of 85 m?<BR>\n" );
document.write( "h(t) = -5t^2 + 15t + 80<BR>\n" );
document.write( "85 =  -5t^2 + 15t + 80<BR>\n" );
document.write( "5t^2-15t+5 = 0<BR>\n" );
document.write( "t^2-3t+1 = 0<BR>\n" );
document.write( "t = [3+-sqrt(9-4*1*1)]/2<BR>\n" );
document.write( "t = [3+-sqrt(5)]/2<BR>\n" );
document.write( "Positive answers:<BR>\n" );
document.write( "t = [3+sqrt5]/2 = 2.62 seconds (on the way down)<BR>\n" );
document.write( "or t =[3-sqrt(5)]/2 = 0.38197 seconds (on the way up)<BR>\n" );
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document.write( "32)Science and Medicine: How long does it take the ball to fall back to the ground?<BR>\n" );
document.write( "Height is zero when the ball is on the ground<BR>\n" );
document.write( "h(t) = -5t^2 + 15t + 80<BR>\n" );
document.write( " -5t^2 + 15t + 80 = 0<BR>\n" );
document.write( "t^2 -3t-16 = 0<BR>\n" );
document.write( "t = [3 +- sqrt(9-4*1*-16)]/2<BR>\n" );
document.write( "t = [3+-sqrt73]/2<BR>\n" );
document.write( "Positive answer:<BR>\n" );
document.write( "t = (3+sqrt73) / 2<BR>\n" );
document.write( "t = 5.77 seconds<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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