document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970516>Question 970516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A model rocket is launched from the ground with an initial velocity of 160 feet/second. How long will it take the rocket to reach maximum height?\r<BR>\n" );
document.write( "\n" );
document.write( "Assume the model rocket's parachute failed to deploy and the rocket fell back to the ground.  How long would it take the rocket to return to earth from the time it was launched? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593132 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=593132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assumptions: \r<BR>\n" );
document.write( "\n" );
document.write( "1) The rocket is starting on the ground (and not on a building or hill)\r<BR>\n" );
document.write( "\n" );
document.write( "2) The rocket comes back to the same ground level (same height) as the starting point.\r<BR>\n" );
document.write( "\n" );
document.write( "3) Dealing with wind/air resistance makes this problem a lot more complicated, so we will ignore those factors.\r<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-%28g%2F2%29t%5E2+%2B+v%5B0%5D%2At+%2B+h%5B0%5D ALIGN=MIDDLE  ALT=\"h+=+-%28g%2F2%29t%5E2+%2B+v%5B0%5D%2At+%2B+h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = height at time t (where both h and t are nonnegative)\r<BR>\n" );
document.write( "\n" );
document.write( "g = acceleration of gravity at sea level (roughly 32 ft/sec^2)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial velocity\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial height\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=h+=+-%28g%2F2%29t%5E2+%2B+v%5B0%5D%2At+%2B+h%5B0%5D ALIGN=MIDDLE  ALT=\"h+=+-%28g%2F2%29t%5E2+%2B+v%5B0%5D%2At+%2B+h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-%2832%2F2%29t%5E2+%2B+160%2At+%2B+0 ALIGN=MIDDLE  ALT=\"h+=+-%2832%2F2%29t%5E2+%2B+160%2At+%2B+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+160t ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+160t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The rocket's max height is when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F%282a%29+=+-160%2F%282%2A%28-16%29%29+=+5 ALIGN=MIDDLE  ALT=\"t+=+-b%2F%282a%29+=+-160%2F%282%2A%28-16%29%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question: How long will it take the rocket to reach maximum height? <BR>\n" );
document.write( "Answer: 5 seconds\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "The rocket hits the ground at height h = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+160t ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+160t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+160t+=+h ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+160t+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+160t+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+160t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in h = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%28t+-+10%29+=+0 ALIGN=MIDDLE  ALT=\"-16t%28t+-+10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t+=+0 ALIGN=MIDDLE  ALT=\"-16t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+10+=+0 ALIGN=MIDDLE  ALT=\"t+-+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10 ALIGN=MIDDLE  ALT=\"t+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The rocket is on the ground at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10 ALIGN=MIDDLE  ALT=\"t+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds. The first time value is the starting point whereas the second time value is the ending point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the rocket starts on the ground at t = 0 seconds, flies up, then comes back down and hits the ground at t = 10 seconds. The total flight time is 10 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question: How long would it take the rocket to return to earth from the time it was launched?<BR>\n" );
document.write( "Answer: 10 seconds<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );