document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181908>Question 1181908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is launched straight upwards with an initial velocity of 80 m/s. The height of the rocket, h, in metres, can be modelled by h = -5t^2 + 80t, where t is the elapsed time in seconds. <BR>\n" );
document.write( "a) Sketch a graph that shows the height of the rocket versus time (Label the following y-intercept, <BR>\n" );
document.write( "vertex, x-intercepts). <BR>\n" );
document.write( "b) After how many seconds does the ball hit the ground? <BR>\n" );
document.write( "c) What is the maximum height reached by rocket? When does it reach this height? <BR>\n" );
document.write( "d) How long does it take for the rocket to reach a height of 275 m?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811858 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(t)=-5t^2+80<BR>\n" );
document.write( "maximum height is at t=-b/2a or -80/-10 or 8 seconds. <BR>\n" );
document.write( "f(8)=-320+640=320 feet.<BR>\n" );
document.write( "since the graph is symmetrical around t=8 seconds,, it hits the ground in 16 seconds.<BR>\n" );
document.write( "-5t^2+80t=275<BR>\n" );
document.write( "-5t^2+80t-275=0<BR>\n" );
document.write( "-5(t^2-16t+55)=0<BR>\n" );
document.write( "(t-11)(t-5)=0<BR>\n" );
document.write( "at 5 seconds.  That is for the first time, which is how I interpret the question, but it also will occur at 11 seconds on the way down.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C20%2C-50%2C350%2C275%2C320%2C-5x%5E2%2B80x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C20%2C-50%2C350%2C275%2C320%2C-5x%5E2%2B80x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );