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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 . 

Can you take it from here?

- Doctor Ian, The Math Forum   
Associated Topics:
High School Physics/Chemistry

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