document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140798>Question 140798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The path of a fallen object is given by the function s= -16t^2+v0t+s0, where v0 represents the initial velocity in ft/sec and s0 represents the initial height. The variable t is time in seconds and s is the height of the object in feet.\r<BR>\n" );
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document.write( "If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40 foot building,how high is the rock after 0.5 seconds? After how many seconds will the rock reach maximum height?\r<BR>\n" );
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document.write( "Ive already answered the first question, i think it is 52 feet. Is this correct?<BR>\n" );
document.write( "How do i set up my equation to answer the second question? (step by step please) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102507 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PART ONE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=+-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D ALIGN=MIDDLE  ALT=\"s=+-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280.5%29=+-16%280.5%29%5E2%2B32%280.5%29%2B40 ALIGN=MIDDLE  ALT=\"s%280.5%29=+-16%280.5%29%5E2%2B32%280.5%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280.5%29=+-16%280.25%29%2B16%2B40 ALIGN=MIDDLE  ALT=\"s%280.5%29=+-16%280.25%29%2B16%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280.5%29=+-4%2B16%2B40 ALIGN=MIDDLE  ALT=\"s%280.5%29=+-4%2B16%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280.5%29=+52 ALIGN=MIDDLE  ALT=\"s%280.5%29=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Yes, you are correct.<BR>\n" );
document.write( "52 feet is the correct height.<BR>\n" );
document.write( "PART TWO\r<BR>\n" );
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document.write( "I'm not sure how advanced you are in mathematics to solve the next part. <BR>\n" );
document.write( "If you have taken calculus, you take the derivative of the function and set it equal to zero. <BR>\n" );
document.write( "If you are using algebra, you can recognize that the equation is the equation of a parabola, find the axis of symmetry, and calculate the maximum there.<BR>\n" );
document.write( "Finally you could plot points and try to find the maximum that way. <BR>\n" );
document.write( "We can do all three.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=+-16t%5E2%2B32t%2B40 ALIGN=MIDDLE  ALT=\"s=+-16t%5E2%2B32t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ds%2Fdt=-32t%2B32=0 ALIGN=MIDDLE  ALT=\"ds%2Fdt=-32t%2B32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t%2B32=0 ALIGN=MIDDLE  ALT=\"-32t%2B32=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum occurs at t=1 second.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29=-16%281%29%2B32%281%29%2B40 ALIGN=MIDDLE  ALT=\"s%281%29=-16%281%29%2B32%281%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29=56 ALIGN=MIDDLE  ALT=\"s%281%29=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=+-16t%5E2%2B32t%2B40 ALIGN=MIDDLE  ALT=\"s=+-16t%5E2%2B32t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The axis of symmetry for the parabola <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In your case,<BR>\n" );
document.write( "a=-16<BR>\n" );
document.write( "b=32<BR>\n" );
document.write( "The axis of symmetry is then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-32%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t=-32%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Just as above, s=56 ft at t=1 sec.<BR>\n" );
document.write( "3. Start at t=0 and solve for s.<BR>\n" );
document.write( "(0.0,40)<BR>\n" );
document.write( "(0.5,52)<BR>\n" );
document.write( "(1.0,56)<BR>\n" );
document.write( "(1.5,52)<BR>\n" );
document.write( "(2.0,40)<BR>\n" );
document.write( "You could also take some points aroung t=1 to prove to yourself that the maximum does occur at t=1.<BR>\n" );
document.write( " </SPAN>\n" );
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