document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234949>Question 234949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this problem=<BR>\n" );
document.write( "Stu lives on the top floor of an apartment building, and Hal lives on a lower floor. Hal's window is 1/4 as high as Stu's. Stu drops a stone from his window. Three seconds later, Hal drops a stone from his window. The two stones hit the ground simultaneously. How high is Stu's window from the ground?<BR>\n" );
document.write( "Thank you for helping me to solve this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173165 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=173165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This <a  rel=nofollow HREF= \"http://www.grc.nasa.gov/WWW/K-12/airplane/mofall.html\" target = \"_blank\">formula</a> for distance of a free falling object might help.\r<BR>\n" );
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document.write( "Stu's on top.\r<BR>\n" );
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document.write( "Hal's below.\r<BR>\n" );
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document.write( "Hal's window is 1/4 as high as Stu's.\r<BR>\n" );
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document.write( "This means that Stu's window is 4 times as high as Hal's.\r<BR>\n" );
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document.write( "Stu drops a stone from his window.\r<BR>\n" );
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document.write( "3 seconds later, Hal drops a stone from his window.\r<BR>\n" );
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document.write( "The 2 stones hit the ground simultaneously.\r<BR>\n" );
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document.write( "How high is Stu's window from the ground?\r<BR>\n" );
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document.write( "The formula that will help solve this problem is:\r<BR>\n" );
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document.write( "D = A * T^2 / 2\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "D = distance in meters.<BR>\n" );
document.write( "A = acceleration of Gravity = 9.8 m/s^2 (meters per second squared).<BR>\n" );
document.write( "T = time in seconds.\r<BR>\n" );
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document.write( "Stu drops his stone first.\r<BR>\n" );
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document.write( "3 seconds later Hal drops his stone.\r<BR>\n" );
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document.write( "The distance that Stu's stone has to travel is 4 times the distance that Hal's stone has to travel.\r<BR>\n" );
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document.write( "If we let D = the distance that Hal's stone has to travel, then the formula for the distance that Hal's stone traveled becomes:\r<BR>\n" );
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document.write( "D = A * T^2 / 2.\r<BR>\n" );
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document.write( "Since Stu's traveled 4 times the distance that Hal's stone traveled, and Stu's stone traveled for 3 more seconds than Stu's stone traveled, then the formula for the distance that Stu's stone traveled becomes:\r<BR>\n" );
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document.write( "4D = A * (T+3)^2 / 2\r<BR>\n" );
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document.write( "We have two formulas that need to be solved simultaneously because the same D and the same T apply to both.\r<BR>\n" );
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document.write( "They are:\r<BR>\n" );
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document.write( "D = (A * T^2 / 2)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "4D = (A * (T+3)^2 / 2)\r<BR>\n" );
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document.write( "We can substitute for D from the first equation and solve for T in the second equation.\r<BR>\n" );
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document.write( "The second equation becomes:\r<BR>\n" );
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document.write( "4*A*T^2 / 2 = A*(T+3)^2 / 2\r<BR>\n" );
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document.write( "We multiply both sides of the equation by 2 and we divide both sides of the equation by A to get:\r<BR>\n" );
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document.write( "4*T^2 = (T+3)^2\r<BR>\n" );
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document.write( "We expand the right side of the equation to get:\r<BR>\n" );
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document.write( "4*T^2 = T^2 + 6*T + 9\r<BR>\n" );
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document.write( "We subtract T^2 + 6*T + 9 from both sides of the equation to get:\r<BR>\n" );
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document.write( "4*T^2 - T^2 - 6*T - 9 = 0\r<BR>\n" );
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document.write( "We combine like terms to get:\r<BR>\n" );
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document.write( "3*T^2 - 6*T - 9 = 0\r<BR>\n" );
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document.write( "We divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "T^2 - 2*T - 3 = 0\r<BR>\n" );
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document.write( "We factor this quadratic equation to get:\r<BR>\n" );
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document.write( "(T-3) * (T+1) = 0\r<BR>\n" );
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document.write( "We solve for T to get:\r<BR>\n" );
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document.write( "T = 3 or T = -1\r<BR>\n" );
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document.write( "Since T can't be negative (T represents time), we get:\r<BR>\n" );
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document.write( "T = 3\r<BR>\n" );
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document.write( "We test this value for T to see if it is good.\r<BR>\n" );
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document.write( "Our original equations are:\r<BR>\n" );
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document.write( "D = (A * T^2) / 2\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "4D = (A * (T+3)^2) / 2\r<BR>\n" );
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document.write( "The first equation becomes D = (A * 3 ^2) / 2 = 9*A/2\r<BR>\n" );
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document.write( "the second equation becomes 4D = (A * 6^2) / 2 = 36*A/2\r<BR>\n" );
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document.write( "We divide the second equation by 4 to get D = 9*A/2\r<BR>\n" );
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document.write( "The equations are identical so the value for T is good.\r<BR>\n" );
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document.write( "We now look to solve for D.\r<BR>\n" );
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document.write( "We know that A = 9.8 meters per second squared.\r<BR>\n" );
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document.write( "Our equations become:\r<BR>\n" );
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document.write( "D = (9.8 * 9) / 2 = 44.1 meters\r<BR>\n" );
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document.write( "4D = (9.8 * 36) / 2 = 176.4 meters\r<BR>\n" );
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document.write( "Stu's window is 176.4 meters from the ground.\r<BR>\n" );
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document.write( "this is 4 times the height of Hal's window which is 44.1 meters from the ground, as it should be.\r<BR>\n" );
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document.write( "The answer to the question is that Stu's window is 176.4 meters from the ground.\r<BR>\n" );
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document.write( "If you look at what has happened, the second by second sequence is shown below, using the formula D = 9.8*T^2:\r<BR>\n" );
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document.write( "Results are truncated to the nearest 10th of a second.\r<BR>\n" );
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document.write( "after 1 second Stu's stone has traveled 4.9 meters <BR>\n" );
document.write( "after 2 seconds Stu's stone has traveled 19.6 meters <BR>\n" );
document.write( "after 3 seconds Stu's stone has traveled 44.1 meters<BR>\n" );
document.write( "after 4 seconds Stu's stone has traveled 78.4 meters<BR>\n" );
document.write( "after 5 seconds Stu's stone has traveled 122.5 meters<BR>\n" );
document.write( "after 6 seconds Stu's stone has traveled 176.4 meters.\r<BR>\n" );
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document.write( "The figures for Hal are:\r<BR>\n" );
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document.write( "after 1 second Hal's stone has traveled 4.9 meters <BR>\n" );
document.write( "after 2 seconds Hal's stone has traveled 19.6 meters <BR>\n" );
document.write( "after 3 seconds Hal's stone has traveled 44.1 meters\r<BR>\n" );
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document.write( "Hal started 3 seconds after Stu.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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