document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=321378>Question 321378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Time in the air. A ball is tossed into the air from a height<BR>\n" );
document.write( "of 12 feet at 16 ft/sec. How long does it take to reach the<BR>\n" );
document.write( "earth?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230172 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=230172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Time in the air. A ball is tossed into the air from a height<BR>\n" );
document.write( "of 12 feet at 16 ft/sec. How long does it take to reach the<BR>\n" );
document.write( "earth? <BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Acceleration due to gravity on Earth is ~-16ft/sec/sec.  Negative because it's down.<BR>\n" );
document.write( "Height as a function of time is<BR>\n" );
document.write( "h(t) = -16t^2 + vt + h0, t in seconds, h in feet<BR>\n" );
document.write( "v is the initial velocity, 16 ft/sec and h0 is the initial height, 12 feet<BR>\n" );
document.write( "h(t) = -16t^2 + 16t + 12<BR>\n" );
document.write( "It impacts when h = 0<BR>\n" );
document.write( "-16t^2 + 16t + 12 = 0<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%2B16x%2B12+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B16x%2B12+=+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=%2816%29%5E2-4%2A-16%2A12=1024 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2816%29%5E2-4%2A-16%2A12=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1024 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+1024+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-16%2B-sqrt%28+1024+%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-%2816%29%2Bsqrt%28+1024+%29%29%2F2%5C-16+=+-0.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+1024+%29%29%2F2%5C-16+=+-0.5\"   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-%2816%29-sqrt%28+1024+%29%29%2F2%5C-16+=+1.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2816%29-sqrt%28+1024+%29%29%2F2%5C-16+=+1.5\"   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%2B16x%2B12 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B16x%2B12\"   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%2B16x%2B12+=+%28x--0.5%29%2A%28x-1.5%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B16x%2B12+=+%28x--0.5%29%2A%28x-1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.5, 1.5.\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%2B16%2Ax%2B12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B16%2Ax%2B12+%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 -0.5 seconds<BR>\n" );
document.write( "t = 1.5 seconds\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );