document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109478>Question 109478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a professional stunt performer at a theme park dives off a tower 21m high into the water. his height above the ground at time t seconds is given by the equation h=-4.9^1/2+211\r<BR>\n" );
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document.write( "how long does it take to reach the water?<BR>\n" );
document.write( "how long does it take to reach the halfway mark? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79816 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=79816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation is incorrect. Assuming that the diver is in free fall (meaning that he<BR>\n" );
document.write( "had no initial velocity) the equation should be:<BR>\n" );
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document.write( "h = -4.9t^2 + 21<BR>\n" );
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document.write( "In which h is the height of the diver in meters and t is the time the diver has fallen. Note<BR>\n" );
document.write( "that at time zero, you can set t equal to zero and the equation reduces to h = 21. This <BR>\n" );
document.write( "means that just before he jumps, the diver is 21 meters above the water ... just as the<BR>\n" );
document.write( "problem tells you he should be. <BR>\n" );
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document.write( "How long does it take to reach the water?  When the diver just reaches the water his height<BR>\n" );
document.write( "is zero. So substitute zero for h and you have:<BR>\n" );
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document.write( "0 = -4.9t^2 + 21<BR>\n" );
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document.write( "Subtract 21 from both sides to get rid of the +21 on the right side and you have:<BR>\n" );
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document.write( "-21 = -4.9t^2<BR>\n" );
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document.write( "now divide both sides by -4.9 and the result is:<BR>\n" );
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document.write( "t^2 = -21/-4.9 = 4.2857<BR>\n" );
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document.write( "Finally, solve for t by taking the square root of both sides to get:<BR>\n" );
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document.write( "t = sqrt(4.28570 = 2.0702 seconds<BR>\n" );
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document.write( "So the diver will hit the water 2.0702 seconds after leaving the platform.<BR>\n" );
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document.write( "When the diver is halfway down, his height will be half of the 21 meters. So the diver's height<BR>\n" );
document.write( "will be 10.5 meters. Substitute this into the height equation and you have:<BR>\n" );
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document.write( "10.5 = -4.9t^2 + 21<BR>\n" );
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document.write( "Subtract 21 from both sides to get rid of the 21 on the right side and you have:<BR>\n" );
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document.write( "-10.5 = -4.9t^2<BR>\n" );
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document.write( "Divide both sides by -4.9 and the result is:<BR>\n" );
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document.write( "t^2 = -10.5/-4.9 = 2.1429 seconds<BR>\n" );
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document.write( "Find t by taking the square root of both sides and you have:<BR>\n" );
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document.write( "t = 1.4639 seconds<BR>\n" );
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document.write( "So in 1.4639 seconds the diver is half way down. And in the remaining time of 0.6063 seconds<BR>\n" );
document.write( "(comes from 2.0702 seconds to fall the entire 21 meters less the 1.4639 seconds to fall<BR>\n" );
document.write( "the first half of the way) the diver falls the rest of the way. His rate of fall is getting<BR>\n" );
document.write( "faster and faster the more time that he is falling.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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