document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950010>Question 950010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the second ball in order to meet the first ball 150 meters from 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 #580041 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=580041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 meters per second, followed by another shot after 5 sec. Find the initial velocity of the second ball in order to meet the first ball 150 meters from the ground.<BR>\n" );
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document.write( "Using 5 m/sec/sec as gravity influence:<BR>\n" );
document.write( "For the 1st ball:<BR>\n" );
document.write( "h(t) = -5t^2 + 80t<BR>\n" );
document.write( "For h(t) = 150<BR>\n" );
document.write( "-5t^2 + 80t = 150<BR>\n" );
document.write( "t^2 - 16t + 30 = 0<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=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=1x%5E2%2B-16x%2B30+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B30+=+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=%28-16%29%5E2-4%2A1%2A30=136 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-16%29%5E2-4%2A1%2A30=136\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=136 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--16%2B-sqrt%28+136+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--16%2B-sqrt%28+136+%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-%28-16%29%2Bsqrt%28+136+%29%29%2F2%5C1+=+13.8309518948453 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+136+%29%29%2F2%5C1+=+13.8309518948453\"   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-%28-16%29-sqrt%28+136+%29%29%2F2%5C1+=+2.1690481051547 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-16%29-sqrt%28+136+%29%29%2F2%5C1+=+2.1690481051547\"   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=1x%5E2%2B-16x%2B30 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B30\"   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=1x%5E2%2B-16x%2B30+=+%28x-13.8309518948453%29%2A%28x-2.1690481051547%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B30+=+%28x-13.8309518948453%29%2A%28x-2.1690481051547%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 13.8309518948453, 2.1690481051547.\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+1%2Ax%5E2%2B-16%2Ax%2B30+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t = 2.169 seconds ascending, less than 5 seconds --> not possible for them to meet.<BR>\n" );
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document.write( "t = 13.831 seconds descending at 150 meters.<BR>\n" );
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document.write( "The 2nd ball has to get to 150 meters in 8.831 seconds (13.831 - 5)<BR>\n" );
document.write( "h(t) = -5t^2 + v*t<BR>\n" );
document.write( "150 = -5*8.831^2 + v*8.831<BR>\n" );
document.write( "8.831v = 539.9328<BR>\n" );
document.write( "v =~ 61.1406 m/sec\r<BR>\n" );
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document.write( " </SPAN>\n" );
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