document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109473>Question 109473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pair of skydivers jump out of an airplane 5.5 km. above the ground. The equation H=5500-5t(square)is an approximate model for divers' altitude in meters at t seconds after jumping out of the plane.\r<BR>\n" );
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document.write( "If a parachute does not open at 1000m, how much time is left to use the emergency chute? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79813 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=79813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given that the equation for the height above ground t seconds after jumping from<BR>\n" );
document.write( "the plane is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+5500+-5t%5E2 ALIGN=MIDDLE  ALT=\"H+=+5500+-5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where H is the height t seconds after jumping out:<BR>\n" );
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document.write( "So let's find out how much time it would take for the skydivers to fall the entire distance<BR>\n" );
document.write( "from the plane to the ground.  When the divers reach the ground their height above ground is<BR>\n" );
document.write( "zero feet. In this case, the time it takes to fall that far is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+5500+-+5t%5E2 ALIGN=MIDDLE  ALT=\"0+=+5500+-+5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this equation by subtracting 5500 from both sides to make the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5500+=+-5t%5E2 ALIGN=MIDDLE  ALT=\"-5500+=+-5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then divide both sides by -5 to get that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1100+=+t%5E2 ALIGN=MIDDLE  ALT=\"1100+=+t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, solve for t by taking the square root of both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+sqrt%281100%29+=+33.166 ALIGN=MIDDLE  ALT=\"t+=+sqrt%281100%29+=+33.166\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the time it takes to fall the 5500 feet from the plane to the ground is 33.166 seconds.<BR>\n" );
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document.write( "But the time that it takes to fall from the plane to the 1000 ft level takes up some of <BR>\n" );
document.write( "that 33.166 seconds. You can solve for that time by substituting 1000 into the height equation<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+5500+-+5t%5E2 ALIGN=MIDDLE  ALT=\"1000+=+5500+-+5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 5500 from both sides to get rid of the 5500 on the right side and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4500+=+-5t%5E2 ALIGN=MIDDLE  ALT=\"-4500+=+-5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by -5 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900+=+t%5E2 ALIGN=MIDDLE  ALT=\"900+=+t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and solve for t by taking the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+t ALIGN=MIDDLE  ALT=\"30+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So if a skydiver jumps from a plane at 5500 feet and falls for 30 seconds he or she is at<BR>\n" );
document.write( "the 1000 ft level. Since that skydiver will hit the ground in a total of 33.166 seconds after <BR>\n" );
document.write( "the jump, there are only 3.166 seconds left to slow the descent (33.166 seconds for the entire <BR>\n" );
document.write( "fall less the 30 seconds that the skydiver fell to get from 5500 feet to 1000 feet).  <BR>\n" );
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document.write( "The answer to your problem is 3.166 seconds.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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