document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378930>Question 378930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A body is thrown vertically upward from the distance h = 1.5 m above the ground at the edge of a pit having a depth of s = 3.5 m<BR>\n" );
document.write( "The initial velocity of body is 2.3 m/s <BR>\n" );
document.write( "Determine the velocity at which the body will reach the bottom of the pit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #269123 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=269123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You didn't give the info, so I'll assume this is on the Earth and use<BR>\n" );
document.write( "h(t) = -4.9t^2 + vt, t in seconds, h in meters<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "h(t) = -16t^2 + 2.3t<BR>\n" );
document.write( "Find t for h(t) = -3.5 meters<BR>\n" );
document.write( "-3.5 = -4.9t^2 + 2.3t<BR>\n" );
document.write( "-4.9t^2 + 2.3t + 3.5 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9x%5E2%2B2.3x%2B3.5+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B2.3x%2B3.5+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%282.3%29%5E2-4%2A-4.9%2A3.5=73.89 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282.3%29%5E2-4%2A-4.9%2A3.5=73.89\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=73.89 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+=+%28-2.3%2B-sqrt%28+73.89+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2.3%2B-sqrt%28+73.89+%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=x%5B1%5D+=+%28-%282.3%29%2Bsqrt%28+73.89+%29%29%2F2%5C-4.9+=+-0.6424417621568 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%282.3%29%2Bsqrt%28+73.89+%29%29%2F2%5C-4.9+=+-0.6424417621568\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%282.3%29-sqrt%28+73.89+%29%29%2F2%5C-4.9+=+1.11182951725884 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%282.3%29-sqrt%28+73.89+%29%29%2F2%5C-4.9+=+1.11182951725884\"   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=-4.9x%5E2%2B2.3x%2B3.5 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B2.3x%2B3.5\"   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=-4.9x%5E2%2B2.3x%2B3.5+=+%28x--0.6424417621568%29%2A%28x-1.11182951725884%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B2.3x%2B3.5+=+%28x--0.6424417621568%29%2A%28x-1.11182951725884%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.6424417621568, 1.11182951725884.\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+-4.9%2Ax%5E2%2B2.3%2Ax%2B3.5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B2.3%2Ax%2B3.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "----------------<BR>\n" );
document.write( "t = 1.1118 seconds (Ignore the negative solution)<BR>\n" );
document.write( "velocity = h'(t) = -9.8t + 2.3<BR>\n" );
document.write( "h'(1.1118) = -8.59564 m/sec at impact (negative = going down)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );