document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172455>Question 1172455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Student A, who is standing in the fourth floor drops the ball from the ledge of the 12-meter building. When the ball is 3 meters above the ground, student B, standing 1.8 meters tall, looks up and notices that the ball is directly above him. How long does student B have to get out of the way? </SPAN>\n" );
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document.write( "We'll ignore air resistance as it greatly complicates the problem. <BR>\n" );
document.write( "We don't have enough info even if we wanted to account for air resistance.\r<BR>\n" );
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document.write( "We'll use the free fall equation which is<BR>\n" );
document.write( "y = 0.5*g*t^2<BR>\n" );
document.write( "the variables are<BR>\n" );
document.write( "y = vertical distance the ball travels<BR>\n" );
document.write( "g = acceleration of gravity<BR>\n" );
document.write( "t = elapsed time\r<BR>\n" );
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document.write( "On earth, the acceleration of gravity is roughly 9.81 m/s^2<BR>\n" );
document.write( "So g = 9.81 approximately\r<BR>\n" );
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document.write( "The free fall equation updates to<BR>\n" );
document.write( "y = 0.5*g*t^2<BR>\n" );
document.write( "y = 0.5*9.81*t^2<BR>\n" );
document.write( "y = 4.905t^2<BR>\n" );
document.write( "which is approximate.\r<BR>\n" );
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document.write( "If student B wasn't in the way, then the ball would travel 12 meters. <BR>\n" );
document.write( "If student B is there, and the ball hits them, then the ball travels 12-1.8 = 10.2 meters\r<BR>\n" );
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document.write( "Let's determine how long it takes for the ball to travel 10.2 meters\r<BR>\n" );
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document.write( "Plug in y = 10.2 and solve for t<BR>\n" );
document.write( "y = 4.905t^2<BR>\n" );
document.write( "10.2 = 4.905t^2<BR>\n" );
document.write( "4.905t^2 = 10.2<BR>\n" );
document.write( "t^2 = 10.2/4.905<BR>\n" );
document.write( "t^2 = 2.07951070336391<BR>\n" );
document.write( "t = sqrt(2.07951070336391)<BR>\n" );
document.write( "t = 1.44205086712082<BR>\n" );
document.write( "t = 1.442\r<BR>\n" );
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document.write( "It takes about 1.442 seconds for the ball to hit student B\r<BR>\n" );
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document.write( "Now let's calculate the time it takes for the ball to travel 12-3 = 9 meters. <BR>\n" );
document.write( "This is the moment in time when student B looks up and sees the ball 3 meters above the ground.\r<BR>\n" );
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document.write( "Plug in y = 9 and solve for t<BR>\n" );
document.write( "y = 4.905t^2<BR>\n" );
document.write( "9 = 4.905t^2<BR>\n" );
document.write( "4.905t^2 = 9<BR>\n" );
document.write( "t^2 = 9/4.905<BR>\n" );
document.write( "t^2 = 1.8348623853211<BR>\n" );
document.write( "t = sqrt(1.8348623853211)<BR>\n" );
document.write( "t = 1.35457092295719<BR>\n" );
document.write( "t = 1.355\r<BR>\n" );
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document.write( "It takes about 1.355 seconds for the ball to drop 9 meters.\r<BR>\n" );
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document.write( "Subtract the time values we calculated<BR>\n" );
document.write( "1.442 - 1.355 = 0.087\r<BR>\n" );
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document.write( "So the student B has approximately 0.087 seconds to react and get out of the way after they spot the ball.\r<BR>\n" );
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document.write( "<font color=red>Answer: approximately 0.087 seconds</font><BR>\n" );
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