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Water Level in a Well


Date: 10/09/2001 at 18:50:14
From: Jason
Subject: Word Problem

A man wishes to determine the water level in a deep well. He drops a 
stone into the well and hears the stone hit the water 3 seconds later.  
If the stone drops 16t^2 feet after t seconds, and the speed of sound 
is 1090 ft/s, how far below the opening of the well is the surface of 
the water (to the nearest foot)?

I tried to apply physics to it.


Date: 10/10/2001 at 12:18:09
From: Doctor Ian
Subject: Re: Word Problem

Hi Jason,

The time (t) required for the stone to hit the water is given by

  d = 16t^2

where d is the distance to the surface of the water.  The time (T) 
required for the sound to come back is given by

  d = (1090)T

which means that

  16t^2 = (1090)T

We're also told that the round trip time (t+T) is 3 seconds, so 

  t + T = 3 

Now you have two equations with two unknowns.  Can you take it from 
here? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
High School Physics/Chemistry

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