document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276918>Question 276918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help. I'm totally perplexed by the question: An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after 6 seconds is given by S(t) = -16t^2 -32t +128.\r<BR>\n" );
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document.write( "What is the height after 1 second? How long does it take for the wrench to reach the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201735 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=201735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's see if we can \"un\"perplex you!<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29+=+-16t%5E2-32%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29+=+-16t%5E2-32%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the quadratic equation that shows the relationship of the height (h or S) of an object as a function of time (t).<BR>\n" );
document.write( "The general form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-%281%2F2%29gt%5E2+%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-%281%2F2%29gt%5E2+%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where h (or S) = height of object, <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;\" >= initial velocity, a negative <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;\" > means object is going down, and <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 of the object, so, to find the height of the object after 1 second, substitute t = 1...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29+=+-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29+=+-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute t=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29+=+-16%281%29%5E2-32%281%29%2B128 ALIGN=MIDDLE  ALT=\"S%281%29+=+-16%281%29%5E2-32%281%29%2B128\"   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+=+-48%2B128 ALIGN=MIDDLE  ALT=\"S%281%29+=+-48%2B128\"   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+=+80 ALIGN=MIDDLE  ALT=\"S%281%29+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet.<BR>\n" );
document.write( "The hammer (or was it a wrench?) would be 80 feet above the ground after 1 second had elapsed.<BR>\n" );
document.write( "The second question...How long does it take for it (the wrench) to reach the ground? So you are really asking...\"At what time t will the height S be zero?\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29+=+-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29+=+-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29+=+0 ALIGN=MIDDLE  ALT=\"S%28t%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-32t%2B128+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2-32t%2B128+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > First factor (-16) to simplify the equation a bit.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%28t%5E2%2B2t-8%29+=+0 ALIGN=MIDDLE  ALT=\"-16%28t%5E2%2B2t-8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, from the zero product rule, we get...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2%2B2t-8+=+0 ALIGN=MIDDLE  ALT=\"t%5E2%2B2t-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor this trinomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2B4%29%28t-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28t%2B4%29%28t-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B4+=+0 ALIGN=MIDDLE  ALT=\"t%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B2+=+0 ALIGN=MIDDLE  ALT=\"t%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > from which we get...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-4 ALIGN=MIDDLE  ALT=\"t+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t+=+2%29 ALIGN=MIDDLE  ALT=\"highlight%28t+=+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard the negative solution.<BR>\n" );
document.write( "So it would take 2 seconds for the wrench to reach the ground.<BR>\n" );
document.write( "P.S. Your statement \"The height of the wrench above the ground after 6 seconds is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29+=+-16t%5E2-32T%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29+=+-16t%5E2-32T%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" does not make sense.  The equation is ok but this will tell you the height above ground after t seconds.<BR>\n" );
document.write( "To find the height above ground after 6 seconds, you would have to substitute t = 6 into the equation and solve for S(6). </SPAN>\n" );
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