document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195679>Question 195679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is launched from atop a 101-foot cliff with an initial velocity of 116ft/s.<BR>\n" );
document.write( "a. Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0<BR>\n" );
document.write( "b.Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched Round to the nearest tenth of a second </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146742 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=146742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The initial velocity is 116 so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+116 ALIGN=MIDDLE  ALT=\"v+=+116\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The initial height is 101 so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+101 ALIGN=MIDDLE  ALT=\"c+=+101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2Bvt%2Bc ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2Bvt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B116t%2B101 ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B116t%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=116 ALIGN=MIDDLE  ALT=\"v=116\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=101 ALIGN=MIDDLE  ALT=\"c=101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B116t%2B101 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B116t%2B101\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (i.e., replace h with 0)\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Refer to part A above.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"0=at%5E2%2Bbt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=116 ALIGN=MIDDLE  ALT=\"b=116\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=101 ALIGN=MIDDLE  ALT=\"c=101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28116%29+%2B-+sqrt%28+%28116%29%5E2-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28116%29+%2B-+sqrt%28+%28116%29%5E2-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=116 ALIGN=MIDDLE  ALT=\"b=116\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=101 ALIGN=MIDDLE  ALT=\"c=101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+sqrt%28+13456-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+sqrt%28+13456-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=116 ALIGN=MIDDLE  ALT=\"116\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13456 ALIGN=MIDDLE  ALT=\"13456\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+sqrt%28+13456--6464+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+sqrt%28+13456--6464+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-16%29%28101%29 ALIGN=MIDDLE  ALT=\"4%28-16%29%28101%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6464 ALIGN=MIDDLE  ALT=\"-6464\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+sqrt%28+13456%2B6464+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+sqrt%28+13456%2B6464+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813456--6464%29 ALIGN=MIDDLE  ALT=\"sqrt%2813456--6464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813456%2B6464%29 ALIGN=MIDDLE  ALT=\"sqrt%2813456%2B6464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13456 ALIGN=MIDDLE  ALT=\"13456\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6464 ALIGN=MIDDLE  ALT=\"6464\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19920 ALIGN=MIDDLE  ALT=\"19920\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116+%2B-+4%2Asqrt%281245%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116+%2B-+4%2Asqrt%281245%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116%2B4%2Asqrt%281245%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116%2B4%2Asqrt%281245%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-116-4%2Asqrt%281245%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-116-4%2Asqrt%281245%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2829-sqrt%281245%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"t+=+%2829-sqrt%281245%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2829%2Bsqrt%281245%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"t+=+%2829%2Bsqrt%281245%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the exact roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2829-sqrt%281245%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"t+=+%2829-sqrt%281245%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2829%2Bsqrt%281245%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"t+=+%2829%2Bsqrt%281245%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.78556969109433 ALIGN=MIDDLE  ALT=\"t=-0.78556969109433\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=8.03556969109433 ALIGN=MIDDLE  ALT=\"t=8.03556969109433\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative time value doesn't make sense, the only practical root is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=8.03556969109433 ALIGN=MIDDLE  ALT=\"t=8.03556969109433\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This rounds to one decimal place to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%228.0%22 ALIGN=MIDDLE  ALT=\"t+=+%228.0%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it takes about 8.0 seconds for the rocket to hit the ground. </SPAN>\n" );
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