document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93468>Question 93468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoity is 204ft/sec, the height is given by h=-16t^2+204t+28 When will the projectile 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 #68049 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=68049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "To find out when the projectile will hit the ground, let h=0 and solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B204t%2B28 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B204t%2B28\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in h=0\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( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2At%5E2%2B204%2At%2B28=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B204%2At%2B28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=204 ALIGN=MIDDLE  ALT=\"b=204\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=28 ALIGN=MIDDLE  ALT=\"c=28\"   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+=+%28-204+%2B-+sqrt%28+%28204%29%5E2-4%2A-16%2A28+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+sqrt%28+%28204%29%5E2-4%2A-16%2A28+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=204, and c=28\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-204+%2B-+sqrt%28+41616-4%2A-16%2A28+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+sqrt%28+41616-4%2A-16%2A28+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 204 to get 41616  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-204+%2B-+sqrt%28+41616%2B1792+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+sqrt%28+41616%2B1792+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A28%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A28%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1792 ALIGN=MIDDLE  ALT=\"1792\"   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+=+%28-204+%2B-+sqrt%28+43408+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+sqrt%28+43408+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-204+%2B-+4%2Asqrt%282713%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+4%2Asqrt%282713%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, 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+=+%28-204+%2B-+4%2Asqrt%282713%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B-+4%2Asqrt%282713%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -16 to get -32\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-204+%2B+4%2Asqrt%282713%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-204+%2B+4%2Asqrt%282713%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-204+-+4%2Asqrt%282713%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-204+-+4%2Asqrt%282713%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-204%2F-32%2B4%2Asqrt%282713%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-204%2F-32%2B4%2Asqrt%282713%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-204%2F-32-4%2Asqrt%282713%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-204%2F-32-4%2Asqrt%282713%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=51+%2F+8-sqrt%282713%29%2F8 ALIGN=MIDDLE  ALT=\"t=51+%2F+8-sqrt%282713%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=51+%2F+8%2Bsqrt%282713%29%2F8 ALIGN=MIDDLE  ALT=\"t=51+%2F+8%2Bsqrt%282713%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.135808321552709 ALIGN=MIDDLE  ALT=\"t=-0.135808321552709\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12.8858083215527 ALIGN=MIDDLE  ALT=\"t=12.8858083215527\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.135808321552709 ALIGN=MIDDLE  ALT=\"t=-0.135808321552709\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12.8858083215527 ALIGN=MIDDLE  ALT=\"t=12.8858083215527\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative time doesn't make sense, our only solution is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12.8858083215527 ALIGN=MIDDLE  ALT=\"t=12.8858083215527\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the projectile will hit the ground at about 12.89 seconds </SPAN>\n" );
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