From What Height Did the Stone Fall?Date: 01/30/2002 at 23:55:31 From: Brian Rho Subject: From what height did the stone fall? A falling stone takes .30 seconds to travel past a window 2.2m tall. From what height above the top of the window did the stone fall? Date: 01/31/2002 at 11:18:36 From: Doctor Ian Subject: Re: From what height did the stone fall? Hi Brian, That's a neat question! There is probably some trick you can use to find the answer more elegantly, but here is how I would approach it. If the stone was simply dropped from some height, the distance it would fall in t seconds would be d = (1/2)gt^2 where g is the acceleration due to gravity, 9.8 m/sec^2. The stone starts passing the window at some time t. It finishes passing the window at some later time T. . . --- . d = (1/2)gt^2 | . t | . T = t + 0.30 seconds | . | . d - d = 2.2 meters | . T t --- . d = (1/2)gT^2 o T We know that the difference in distances is 2.2 meters, so (1/2)gT^2 - (1/2)gt^2 = 2.2 And we know that the difference in time is 0.30 seconds, so T = t + 0.30 Now you can substitute for T in the first equation, solve for t, and use the value of t to find d . t Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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