document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180053>Question 180053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a cartoon , a malfunctioning cannon fires a hungry coyote towards the bottom of a cliff with an initial rate of 100 feet per second. If the cliff is 1250 feet tall , how long will it take the coyote to reach the desert floor? (To account for gravity, use the formula d =rt + 16t^2, where d =distance, r = initial rate, and t = time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134911 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=134911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     In a cartoon , a malfunctioning cannon fires a hungry coyote towards the bottom of a cliff with an initial rate of 100 feet per second. If the cliff is 1250 feet tall , how long will it take the coyote to reach the desert floor? (To account for gravity, use the formula d =rt + 16t^2, where d =distance, r = initial rate, and t = time.<BR>\n" );
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document.write( "From your problem, you are given:<BR>\n" );
document.write( "d = 1250 feet<BR>\n" );
document.write( "r = 1000 ft/sec<BR>\n" );
document.write( "t is what we're looking for...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Plug in the provided values and solve for t:<BR>\n" );
document.write( "d =rt + 16t^2<BR>\n" );
document.write( "1250 = 1000t + 16t^2<BR>\n" );
document.write( "625 = 500t + 8t^2<BR>\n" );
document.write( "0 = 500t + 8t^2 - 625<BR>\n" );
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document.write( "Using the quadratic equation, we get:<BR>\n" );
document.write( "x = {1.110, -1.126}<BR>\n" );
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document.write( "We can toss out the negative solution leaving us with:<BR>\n" );
document.write( "x = 1.110 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic follows:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500t%5E2%2B8t%2B-625+=+0 ALIGN=MIDDLE  ALT=\"500t%5E2%2B8t%2B-625+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%288%29%5E2-4%2A500%2A-625=1250064 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A500%2A-625=1250064\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1250064 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-8%2B-sqrt%28+1250064+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+1250064+%29%29%2F2%5Ca\"   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=t%5B1%5D+=+%28-%288%29%2Bsqrt%28+1250064+%29%29%2F2%5C500+=+1.11006261005366 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%288%29%2Bsqrt%28+1250064+%29%29%2F2%5C500+=+1.11006261005366\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%288%29-sqrt%28+1250064+%29%29%2F2%5C500+=+-1.12606261005366 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%288%29-sqrt%28+1250064+%29%29%2F2%5C500+=+-1.12606261005366\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500t%5E2%2B8t%2B-625 ALIGN=MIDDLE  ALT=\"500t%5E2%2B8t%2B-625\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500t%5E2%2B8t%2B-625+=+500%28t-1.11006261005366%29%2A%28t--1.12606261005366%29 ALIGN=MIDDLE  ALT=\"500t%5E2%2B8t%2B-625+=+500%28t-1.11006261005366%29%2A%28t--1.12606261005366%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.11006261005366, -1.12606261005366.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+500%2Ax%5E2%2B8%2Ax%2B-625+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+500%2Ax%5E2%2B8%2Ax%2B-625+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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