document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136257>Question 1136257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> NASA launches a rocker at T=0 seconds. It's height, in meters above sea level, as a function of time is given by H(T)=-4.9T^2 + 229T +185. \r<BR>\n" );
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document.write( "Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? <BR>\n" );
document.write( "The rocket splashes down after ___ seconds\r<BR>\n" );
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document.write( "How high above sea-level does the rocket get at its peak? <BR>\n" );
document.write( "The rocket peaks at ___ meters above sea-level\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754038 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=754038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ASA launches a rocker at T=0 seconds. It's height, in meters above sea level, as a function of time is given by H(T)=-4.9T^2 + 229T +185. \r<BR>\n" );
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document.write( "Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? <BR>\n" );
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document.write( "it's = it is.<BR>\n" );
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document.write( "I would solve the problem, but these entries irritate me.<BR>\n" );
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document.write( "The rocket splashes down after ___ seconds<BR>\n" );
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document.write( "How high above sea-level does the rocket get at its peak? <BR>\n" );
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document.write( "The rocket peaks at ___ meters above sea-level<BR>\n" );
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document.write( "this is not useful.<BR>\n" );
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document.write( "H(T)=-4.9T^2 + 229T +185<BR>\n" );
document.write( "At impact, h(t) = 0<BR>\n" );
document.write( "-4.9T^2 + 229T +185 = 0<BR>\n" );
document.write( "Solve for t<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=-4.9x%5E2%2B229x%2B185+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B229x%2B185+=+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=%28229%29%5E2-4%2A-4.9%2A185=56067 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28229%29%5E2-4%2A-4.9%2A185=56067\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=56067 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+=+%28-229%2B-sqrt%28+56067+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-229%2B-sqrt%28+56067+%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-%28229%29%2Bsqrt%28+56067+%29%29%2F2%5C-4.9+=+-0.794358402485433 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28229%29%2Bsqrt%28+56067+%29%29%2F2%5C-4.9+=+-0.794358402485433\"   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-%28229%29-sqrt%28+56067+%29%29%2F2%5C-4.9+=+47.5290522800364 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28229%29-sqrt%28+56067+%29%29%2F2%5C-4.9+=+47.5290522800364\"   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%2B229x%2B185 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B229x%2B185\"   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%2B229x%2B185+=+%28x--0.794358402485433%29%2A%28x-47.5290522800364%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B229x%2B185+=+%28x--0.794358402485433%29%2A%28x-47.5290522800364%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.794358402485433, 47.5290522800364.\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%2B229%2Ax%2B185+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B229%2Ax%2B185+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative value.<BR>\n" );
document.write( "t = ~ 47.529 seconds<BR>\n" );
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document.write( "The peak (max height) is the vertex of the parabola, at t = -b/2a<BR>\n" );
document.write( "t = -229/-9.8 = ~ 23.367 seconds<BR>\n" );
document.write( "h(23.367) =~ 2675.5 meters<BR>\n" );
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document.write( "PS - this is not a rocket, it's a projectile.<BR>\n" );
document.write( "Rockets accelerate upward. </SPAN>\n" );
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