document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029190>Question 1029190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You throw the rocket up in the air with an initial velocity of 50 feet per second, and the rocket leaves your hand 6 feet above the ground. if you catch it when it falls back to a height of 5 feet, how long was the rocket in the air? does the increase in initial velocity increase or decrease the air time of the rocket?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644277 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=644277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You throw the rocket up in the air with an initial velocity of 50 feet per second, and the rocket leaves your hand 6 feet above the ground. if you catch it when it falls back to a height of 5 feet, how long was the rocket in the air? does the increase in initial velocity increase or decrease the air time of the rocket? <BR>\n" );
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document.write( "You didn't spec acceleration due to gravity.<BR>\n" );
document.write( "-32 ft/sec/sec is commonly used.<BR>\n" );
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document.write( "h(t) = gt^2/2 + vt + h0 where g is gravity, v = 50 ft/sec, h0 = 6 feet<BR>\n" );
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document.write( "h(t) = -16t^2 + 50t + 6 : h(t) = height in feet, t = seconds<BR>\n" );
document.write( "Solve for t when h(t) = 5<BR>\n" );
document.write( "h(t) = -16t^2 + 50t + 6 = 5<BR>\n" );
document.write( "-16t^2 + 50t + 1 = 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=-16x%5E2%2B50x%2B1+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B50x%2B1+=+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=%2850%29%5E2-4%2A-16%2A1=2564 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2850%29%5E2-4%2A-16%2A1=2564\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2564 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+=+%28-50%2B-sqrt%28+2564+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-50%2B-sqrt%28+2564+%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-%2850%29%2Bsqrt%28+2564+%29%29%2F2%5C-16+=+-0.0198736126465204 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2850%29%2Bsqrt%28+2564+%29%29%2F2%5C-16+=+-0.0198736126465204\"   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-%2850%29-sqrt%28+2564+%29%29%2F2%5C-16+=+3.14487361264652 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2850%29-sqrt%28+2564+%29%29%2F2%5C-16+=+3.14487361264652\"   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%2B50x%2B1 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B50x%2B1\"   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%2B50x%2B1+=+%28x--0.0198736126465204%29%2A%28x-3.14487361264652%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B50x%2B1+=+%28x--0.0198736126465204%29%2A%28x-3.14487361264652%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0198736126465204, 3.14487361264652.\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%2B50%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B50%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative solution<BR>\n" );
document.write( "t =~ 3.145 seconds </SPAN>\n" );
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