document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120868>Question 120868</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131953648/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help solve for this  problem it has 4 parts?  I don't know where to start.\r<BR>\n" );
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document.write( "The path of a falling 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 the s is the height of the object in feet. <BR>\n" );
document.write( "a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.\r<BR>\n" );
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document.write( "b) How high is the rock after 0.5 seconds?\r<BR>\n" );
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document.write( "c) After how many sections will the rock reach maximum height?\r<BR>\n" );
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document.write( "d)What is the maximum height?\r<BR>\n" );
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document.write( "Please show all work<BR>\n" );
document.write( "Thanks in advance for your help.  \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88672 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29=-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D ALIGN=MIDDLE  ALT=\"s%28t%29=-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a.  You are given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D=32 ALIGN=MIDDLE  ALT=\"v%5B0%5D=32\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B0%5D=40 ALIGN=MIDDLE  ALT=\"s%5B0%5D=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so just plug in the values:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29=-16t%5E2%2B32t%2B40 ALIGN=MIDDLE  ALT=\"s%28t%29=-16t%5E2%2B32t%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.  You need to evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280.5%29 ALIGN=MIDDLE  ALT=\"s%280.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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%2B32%280.5%29%2B40 ALIGN=MIDDLE  ALT=\"s%280.5%29=-16%280.25%29%2B32%280.5%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "So the height (measured from the ground) after one-half second is 52 feet.\r<BR>\n" );
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document.write( "c.  This is a quadratic equation and if you graphed it on a coordinate plane with s as the vertical axis and t as the horizontal axis, you would have a convex down parabola.  The maximum height will be reached at time equal to the value of t at the vertex of the parabola.\r<BR>\n" );
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document.write( "The vertex of any parabola described by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > is located at <b><big>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a%29 ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%28-b%29%2F2a%29 ALIGN=MIDDLE  ALT=\"f%28%28-b%29%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)</b></big>\r<BR>\n" );
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document.write( "For this problem, <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=32 ALIGN=MIDDLE  ALT=\"b=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bmaxh%5D=%28-32%29%2F%282%2A%28-16%29%29=%28-32%29%2F-32=1 ALIGN=MIDDLE  ALT=\"t%5Bmaxh%5D=%28-32%29%2F%282%2A%28-16%29%29=%28-32%29%2F-32=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > second.\r<BR>\n" );
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document.write( "You can also do this part with the calculus\r<BR>\n" );
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document.write( "A local minimum or maximum is found where the first derivative equals 0.\r<BR>\n" );
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document.write( "For this problem, s'(t)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t%2B32 ALIGN=MIDDLE  ALT=\"-32t%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so if <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;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To determine if this is a maximum or minimum, evaluate the second derivative at the same value\r<BR>\n" );
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document.write( "s\"(t)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the second derivitive is less than zero, this is a maximum.\r<BR>\n" );
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document.write( "d. The actual maximum height is just the function evaluated at the time for maximum height, i.e. 1 second, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29 ALIGN=MIDDLE  ALT=\"s%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29=-16%2B32%2B40 ALIGN=MIDDLE  ALT=\"s%281%29=-16%2B32%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;\" >\r<BR>\n" );
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document.write( "And the maximum height is 56 feet. </SPAN>\n" );
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