document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=820472>Question 820472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A model rocket is launched (from the ground s0=0) with an initial velocity (V0) of 320 ft./sec.<BR>\n" );
document.write( "a. Find the Position equation for the rocket<BR>\n" );
document.write( "b. How high did the rocket get? (find the y coordinate of the vertex)<BR>\n" );
document.write( "c. How long did the rocket take to reach its maximum height? (find the x coordinate of the vertex)<BR>\n" );
document.write( "d. How long did the rocket take to return to earth?<BR>\n" );
document.write( "e. How fast was the rocket going when it hit the ground?\r<BR>\n" );
document.write( "\n" );
document.write( "I am very lost on this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493595 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=493595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "The equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%28x%29+=+-16x%5E2+%2B+320x+ ALIGN=MIDDLE  ALT=\"+y%28x%29+=+-16x%5E2+%2B+320x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with a maximum that<BR>\n" );
document.write( "begins at ( x,y ) = ( 0,0 )<BR>\n" );
document.write( "The squared term is entirely the<BR>\n" );
document.write( "effect of gravity pulling the rocket down<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "The x-coordinate of the vertex is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+320+ ALIGN=MIDDLE  ALT=\"+b+=+320+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-320+%2F+%28+2%2A%28-16%29+%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-320+%2F+%28+2%2A%28-16%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-320%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-320%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+10+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "To find the y-coordinate of the vertex, plug<BR>\n" );
document.write( "this value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%28x%29+=+-16x%5E2+%2B+320x+ ALIGN=MIDDLE  ALT=\"+y%28x%29+=+-16x%5E2+%2B+320x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2810%29+=+-16%2A%2810%29%5E2+%2B+320%2A%2810%29+ ALIGN=MIDDLE  ALT=\"+y%2810%29+=+-16%2A%2810%29%5E2+%2B+320%2A%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2810%29+=+-1600+%2B+3200+ ALIGN=MIDDLE  ALT=\"+y%2810%29+=+-1600+%2B+3200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%2810%29+=+1600+ ALIGN=MIDDLE  ALT=\"+y%2810%29+=+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum height is 1600 ft<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "The rocket took 10 sec to reach the maximum height<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "You have to find out when the height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%28x%29+ ALIGN=MIDDLE  ALT=\"+y%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "is zero again, so you have to find both roots<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%28x%29+=+-16x%5E2+%2B+320x+ ALIGN=MIDDLE  ALT=\"+y%28x%29+=+-16x%5E2+%2B+320x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-16x%5E2+%2B+320x+=+0+ ALIGN=MIDDLE  ALT=\"++-16x%5E2+%2B+320x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2A%28+-16x+%2B+320+%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%2A%28+-16x+%2B+320+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16x+%2B+320+=+0+ ALIGN=MIDDLE  ALT=\"+-16x+%2B+320+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16x+=+320+ ALIGN=MIDDLE  ALT=\"+16x+=+320+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+20+ ALIGN=MIDDLE  ALT=\"+x+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rocket took 20 sec to come back to earth<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(e)<BR>\n" );
document.write( "The velocity when it hit the ground is the same as it<BR>\n" );
document.write( "was at takeoff, 320 ft/sec<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Here's a plot of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+25%2C+-200%2C+2000%2C+-16x%5E2+%2B+320x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+25%2C+-200%2C+2000%2C+-16x%5E2+%2B+320x+%29+\"   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( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );