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Kinematics Question

 
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narik



Joined: 08 Nov 2009
Posts: 1
Location: canada

PostPosted: Sun Nov 08, 2009 11:11 pm    Post subject: Kinematics Question Reply with quote

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
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Wed Nov 18, 2009 11:17 pm    Post subject: Reply with quote

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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