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Question

A man standing in front of a vertical cliff fires a gun and hears the echo after 4 seconds. He moves 150 m towards the cliff and again fires the gun. This time, he hears the echo after 3.6 seconds. Find the distance of the cliff from his first position.


A

7500 m

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B

750 m

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C

550 m

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D

1500 m

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Solution

The correct option is D

1500 m


Given:
Time to hear first echo, t1=4 s
Time to hear second echo, t2=3.6 s
Distance between first and second source locations, s=150 m

Let the distance of cliff from the first location be d
Let the velocity of sound be v

Since echo is a reflection of the original sound, it will travel distance equal to twice the distance between man and cliff i.e., 2d.
From definition of speed,
v=2dt1 ...........(i)

Now, after travelling 150 m towards the cliff, distance travelled by sound, d2=2(d150)=2d300
Again from definition of speed,
v=2d300t2 ................(ii)

Equating the value of v from equations (i) and (ii), we get:
2d300t1=2dt2
2d3003.6=2d4

Solving the above equation, we get
d=1500 m

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