Question

A man standing in front of a vertical cliff fires a gun. He hears the echo after 3.5 s. On moving closer to the cliff by 84 m, he hears the echo after 3 s. Calculate the distance of the cliff from the initial position of the man.

Answer 1

Given Data:

Initial echo time (t₁) = 3.5 s

Distance moved closer = 84 m

New echo time (t₂) = 3 s

Let the initial distance of the man from the cliff be d meters, and the speed of sound be m s⁻¹.

Calculation:

Case 1 (Initial Position):

2d = v × t₁

2d = v × 3.5

v = `(2d)/3.5`   .........(1)

Case 2 (After moving 84 m closer):

New distance = (d − 84) m

2(d − 84) = v × t₂

2(d − 84) = v × 3  .........(2)

Substitute the value of (v) from equation (1) into equation (2):

`2(d - 84) = ((2d)/3.5) xx 3`

Divide both sides by 2:

`d - 84 = (3d)/3.5`

Multiply both sides by 3.5:

3.5(d − 84) = 3d

3.5d − 294 = 3d

3.5d − 3d = 294

0.5d = 294

d = `294/0.5`

d = 588 m

The distance of the cliff from the initial position of the man is 588 m.