document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190294>Question 190294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A signal flare is fired upward with initial speed 245m/s.  A stationary balloonist at the height of 1960 m sees the flare pass on the way up.  How long after this will the flare pass the balloonist again on the way down?\r<BR>\n" );
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document.write( "This is for my son, and yes, I'm a few years out of practice. He's tried setting it to zero with: -4.9t^2-245t+1960=0. I think h=rt-4.9t^2 is the formula was also given to him. Can you help, please? He knows the answer is 30 seconds, but can't show the work. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142808 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=142808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, first off, the equation should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%5E2%2B245t=1960 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B245t=1960\"   DISABLED_style= \"max-width:90%; height:auto;\" > (let me know if you need help figuring out the equation)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%5E2%2B245t=1960 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B245t=1960\"   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=-4.9t%5E2%2B245t-1960=0 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B245t-1960=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1960 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-49t%5E2%2B2450t-19600=0 ALIGN=MIDDLE  ALT=\"-49t%5E2%2B2450t-19600=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by 10 to make every number a whole number.\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=at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"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=-49 ALIGN=MIDDLE  ALT=\"a=-49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2450 ALIGN=MIDDLE  ALT=\"b=2450\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-19600 ALIGN=MIDDLE  ALT=\"c=-19600\"   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-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%282450%29+%2B-+sqrt%28+%282450%29%5E2-4%28-49%29%28-19600%29+%29%29%2F%282%28-49%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-49 ALIGN=MIDDLE  ALT=\"a=-49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2450 ALIGN=MIDDLE  ALT=\"b=2450\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-19600 ALIGN=MIDDLE  ALT=\"c=-19600\"   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+=+%28-2450+%2B-+sqrt%28+6002500-4%28-49%29%28-19600%29+%29%29%2F%282%28-49%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B-+sqrt%28+6002500-4%28-49%29%28-19600%29+%29%29%2F%282%28-49%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2450 ALIGN=MIDDLE  ALT=\"2450\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6002500 ALIGN=MIDDLE  ALT=\"6002500\"   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+=+%28-2450+%2B-+sqrt%28+6002500-3841600+%29%29%2F%282%28-49%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B-+sqrt%28+6002500-3841600+%29%29%2F%282%28-49%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-49%29%28-19600%29 ALIGN=MIDDLE  ALT=\"4%28-49%29%28-19600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3841600 ALIGN=MIDDLE  ALT=\"3841600\"   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+=+%28-2450+%2B-+sqrt%28+2160900+%29%29%2F%282%28-49%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B-+sqrt%28+2160900+%29%29%2F%282%28-49%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3841600 ALIGN=MIDDLE  ALT=\"3841600\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6002500 ALIGN=MIDDLE  ALT=\"6002500\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2160900 ALIGN=MIDDLE  ALT=\"2160900\"   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+=+%28-2450+%2B-+sqrt%28+2160900+%29%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B-+sqrt%28+2160900+%29%29%2F%28-98%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=-49 ALIGN=MIDDLE  ALT=\"-49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-98 ALIGN=MIDDLE  ALT=\"-98\"   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+=+%28-2450+%2B-+1470%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B-+1470%29%2F%28-98%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2160900 ALIGN=MIDDLE  ALT=\"2160900\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1470 ALIGN=MIDDLE  ALT=\"1470\"   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+=+%28-2450+%2B+1470%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+%2B+1470%29%2F%28-98%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-2450+-+1470%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=+%28-2450+-+1470%29%2F%28-98%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+=+%28-980%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=+%28-980%29%2F%28-98%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-3920%29%2F%28-98%29 ALIGN=MIDDLE  ALT=\"t+=++%28-3920%29%2F%28-98%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10 ALIGN=MIDDLE  ALT=\"t+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40 ALIGN=MIDDLE  ALT=\"t+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10 ALIGN=MIDDLE  ALT=\"t+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40 ALIGN=MIDDLE  ALT=\"t+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "This means that at 10 seconds the flare is at the height of 1960 m. Also, the flare is 1960 m high when the time is 40 seconds. \r<BR>\n" );
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document.write( "So the difference between these two times is 40-10=30 seconds (think of t=10 as time zero for the balloonist)\r<BR>\n" );
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document.write( "So it takes 30 seconds for the flare to come back down to the height of 1960 m. </SPAN>\n" );
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