document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150020>Question 150020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 13. (8 pts) If a projectile is launched from a platform 40 feet high with an initial velocity of 96 feet per second, then the height of the projectile at t seconds is given by\r<BR>\n" );
document.write( "\n" );
document.write( "s(t) = –16t^2 + 96t + 40 feet.\r<BR>\n" );
document.write( "\n" );
document.write( "	(i) At what time does the projectile attain its maximum height? Show some work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "	(ii) What is the maximum height attained by the projectile? Show some work.\r<BR>\n" );
document.write( "\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 #110109 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=110109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In order to find the time it takes to reach the max height, use this formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16t%5E2%2B96t%2B40 ALIGN=MIDDLE  ALT=\"y=-16t%5E2%2B96t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=96 ALIGN=MIDDLE  ALT=\"b=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=40 ALIGN=MIDDLE  ALT=\"c=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-%2896%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t=%28-%2896%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=96 ALIGN=MIDDLE  ALT=\"b=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So it takes 3 seconds for the projectile to attain its maximum height.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ii)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find the max height, simply plug the time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16t%5E2%2B96t%2B40 ALIGN=MIDDLE  ALT=\"y=-16t%5E2%2B96t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16t%5E2%2B96t%2B40 ALIGN=MIDDLE  ALT=\"y=-16t%5E2%2B96t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16%283%29%5E2%2B96%283%29%2B40 ALIGN=MIDDLE  ALT=\"y=-16%283%29%5E2%2B96%283%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16%289%29%2B96%283%29%2B40 ALIGN=MIDDLE  ALT=\"y=-16%289%29%2B96%283%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-144%2B96%283%29%2B40 ALIGN=MIDDLE  ALT=\"y=-144%2B96%283%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-144 ALIGN=MIDDLE  ALT=\"-144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-144%2B288%2B40 ALIGN=MIDDLE  ALT=\"y=-144%2B288%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96 ALIGN=MIDDLE  ALT=\"96\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=288 ALIGN=MIDDLE  ALT=\"288\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=184 ALIGN=MIDDLE  ALT=\"y=184\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the max height is 184 feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );