document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141673>Question 141673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A model rocket is shot straight up from the roof of a school.  The height at any time t is approximated by the model H=15 + 23t - 5t^2,where H is the height in metres and t is the time in seconds.<BR>\n" );
document.write( "a)how long does it take for the rocket to pass a window 10 m above the ground.<BR>\n" );
document.write( "b) when does the rocket hit the ground?<BR>\n" );
document.write( "c) what is the maximum height the rocket reaches above the roof of the school? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103224 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=103224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H=15 + 23t - 5t^2,where H is the height in metres and t is the time in seconds.<BR>\n" );
document.write( "a)how long does it take for the rocket to pass a window 10 m above the ground.<BR>\n" );
document.write( "-5t^2+23t+15 = 10<BR>\n" );
document.write( "-5t^2+23t+5 = 0<BR>\n" );
document.write( "t = [-23 +- sqrt(23^2-4*-5*5)]/(-10)<BR>\n" );
document.write( "t = [-23 +- sqrt(629)<BR>\n" );
document.write( "t = [-23-25.07987..]/(-10) <BR>\n" );
document.write( "t =  -48.07987]/(-10)<BR>\n" );
document.write( "t = 4.80798 seconds<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Comment: The rocket is at 15 meters when it is launched.<BR>\n" );
document.write( "It arrives at a height of 10 m after 4.80798 seconds on<BR>\n" );
document.write( "its way down to the ground.<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "b) when does the rocket hit the ground?<BR>\n" );
document.write( "-5t^2+23t+15 = 0<BR>\n" );
document.write( "t = [-23 +- sqrt(23^2-4*-1*15)]/(-10)<BR>\n" );
document.write( "t = [-23 +- sqrt(829)]/(-10)<BR>\n" );
document.write( "t = [-23 +- 28.7924..]/(-10)<BR>\n" );
document.write( "t = 5.17924 seconds<BR>\n" );
document.write( "-----------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "c) what is the maximum height the rocket reaches above the roof of the school?<BR>\n" );
document.write( "Max occurs when t = -b/2a = -23/(-10) = 2.3 seconds<BR>\n" );
document.write( "H(t) =15 + 23t - 5t^2<BR>\n" );
document.write( "H(2.3) = 15 + 23*2.3 - 5(2.3)^2<BR>\n" );
document.write( "H(2.3) = 41.45 m<BR>\n" );
document.write( "That is 41.45 - 15 = 26.45 m above the root of the school.<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );