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narik
Joined: 08 Nov 2009 Posts: 1 Location: canada

Posted: Sun Nov 08, 2009 11:11 pm Post subject: Kinematics Question 


A rock is dropped from a seacliff and the sound of it striking the ocean is heard 3.0 s later. If the speed of sound is 340 m/s, how high is the cliff?
I know that t1+t2=3, but I don't know the rest. 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Wed Nov 18, 2009 11:17 pm Post subject: 


The time is known and consists of the time it takes for the rock to fall and the time it take for the sound to reach the observer.
ie. t1 + t2 = 3s.
We know that the rock starts from zero velocity and it is accelerated under gravity. i.e u=0 and a =9.81 ms^2.
From the equations of linear motion,
s = ut + 1/2 at^2 or
s = (1/2) a t^2 since u = 0.
Rearranging, t = (2s/a)^(1/2)
t is our t1.
Therefore,
(2s/a)^(1/2) + t2 = 3
The time t2 taken for the sound to reach the ear is the distance falllen s /(340 ms^1)
Therefore,
(2s/a)^(1/2) + s/340 = 3
It is then simple to substitute the numbers and Bob's your uncle you get the height of the cliff, s. 

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