document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047694>Question 1047694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a body travels half its total path in the last 1.70 s of its fall from rest, find the total time of its fall (in seconds). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663260 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "the equation for distance of a free falling object is:\r<BR>\n" );
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document.write( "d = g * t^2 / 2\r<BR>\n" );
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document.write( "d is the distance traveled.<BR>\n" );
document.write( "g is the acceleration due to gravity which can be rounded to 9.8 meters per second squared.<BR>\n" );
document.write( "t is the time in seconds.\r<BR>\n" );
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document.write( "let d1 = g * t^2 / 2\r<BR>\n" );
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document.write( "let d2 = g * (t + 1.7)^2 / 2\r<BR>\n" );
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document.write( "since d2 is the total distance traveled, then d2 must be equal to 2 * d1.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "d1 = g * t^2 / 2<BR>\n" );
document.write( "2 * d1 = g * (t + 1.7)^2 / 2\r<BR>\n" );
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document.write( "since d1 = g * t^2 / 2, then 2 * d1 is equal to 2 * g * t^2 / 2\r<BR>\n" );
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document.write( "you have 2 * d1 = g * (t + 1.7)^2 / 2 and you have 2 * d1 = 2 * g * t^2 / 2\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "2 * g * t^2 / 2 is equal to g * (t + 1.7)^2 / 2\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "g * t^2 = g * (t + 1.7)^2 / 2\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "g * t^2 = g * (t^2 + 3.4 * t + 2.89) / 2\r<BR>\n" );
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document.write( "multiply both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "2 * g * t^2 = g * (t^2 + 3.4 * t + 2.89)\r<BR>\n" );
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document.write( "divide both sides of this equation by g to get:\r<BR>\n" );
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document.write( "2 * t^2 = t^2 + 3.4 * t + 2.89\r<BR>\n" );
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document.write( "subtract all terms on the right side of the equation from both sides of the equation and you will get:\r<BR>\n" );
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document.write( "2 * t^2 - t^2 - 3.4 * t - 2.89 = 0\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "t^2 - 3.4 * t - 2.89 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "t = -.70416 or t = 4.1042\r<BR>\n" );
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document.write( "t can't be negative, so t = 4.1042 seconds.\r<BR>\n" );
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document.write( "that is the time it took for the first half of the distance.\r<BR>\n" );
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document.write( "the time it took for the second half of the distance is 1.7 seconds.\r<BR>\n" );
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document.write( "the time it took for the total distance is therefore 5.8042 seconds (4.1042 + 1.7).\r<BR>\n" );
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document.write( "to see if this is correct, substitute in the original equation.\r<BR>\n" );
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document.write( "d1 = g * t^2 / 2 becomes d1 = 9.8 * 4.1042^2 / 2 = 82.53784244 meters.\r<BR>\n" );
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document.write( "d2 = g * (t + 1.7)^2 / 2 becomes d2 = 9.l8 * 5.8042^2 / 2 = 165.0748144 meters.\r<BR>\n" );
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document.write( "it traveled 82.53784244 meters in 4.1042 seconds and it traveled 165.0748144 meters in 5.8042 seconds.\r<BR>\n" );
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document.write( "in the last 1.7 seconds of its fall, it traveled 165.0748144 - 82.53784244 meters which is equal to 82.536972 meters.\r<BR>\n" );
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document.write( "that's very close to 82.53784244 meters.\r<BR>\n" );
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document.write( "the difference is due to rounding.\r<BR>\n" );
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document.write( "a more exact definition of the acceleration due to gravity is 9.80665 meters per second squared.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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