document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=616574>Question 616574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second.  About <BR>\n" );
document.write( "how long will it take the ball Amir pitched to hit 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 #387751 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=387751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second.  About <BR>\n" );
document.write( "how long will it take the ball Amir pitched to hit the ground?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The equation commonly used is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+vt+%2B+h ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+vt+%2B+h\"   DISABLED_style= \"max-width:90%; height:auto;\" > where v = vertical speed and h = initial height<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At impact, h(t) = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9+=+0 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=-16x%5E2%2B73.16x%2B5.9+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B73.16x%2B5.9+=+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=%2873.16%29%5E2-4%2A-16%2A5.9=5729.9856 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2873.16%29%5E2-4%2A-16%2A5.9=5729.9856\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5729.9856 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+=+%28-73.16%2B-sqrt%28+5729.9856+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-73.16%2B-sqrt%28+5729.9856+%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-%2873.16%29%2Bsqrt%28+5729.9856+%29%29%2F2%5C-16+=+-0.0792708860840778 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2873.16%29%2Bsqrt%28+5729.9856+%29%29%2F2%5C-16+=+-0.0792708860840778\"   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-%2873.16%29-sqrt%28+5729.9856+%29%29%2F2%5C-16+=+4.65177088608408 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2873.16%29-sqrt%28+5729.9856+%29%29%2F2%5C-16+=+4.65177088608408\"   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=-16x%5E2%2B73.16x%2B5.9 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B73.16x%2B5.9\"   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=-16x%5E2%2B73.16x%2B5.9+=+%28x--0.0792708860840778%29%2A%28x-4.65177088608408%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B73.16x%2B5.9+=+%28x--0.0792708860840778%29%2A%28x-4.65177088608408%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0792708860840778, 4.65177088608408.\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+-16%2Ax%5E2%2B73.16%2Ax%2B5.9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B73.16%2Ax%2B5.9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "-----------<BR>\n" );
document.write( "Ignore the negative solution<BR>\n" );
document.write( "t =~ 4.652 seconds </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );