Question

A man moving towards a vertical cliff at a constant velocity of $u$ $m{s}^{-1}$, fires a gun and hears the echo after $t$ seconds. If he was at a distance of $d$ meters from the cliff when he fired the gun, then the velocity of sound in air in $m{s}^{-1}$ is

• A. $\frac{2d}{t}$
• B. $\frac{2d}{t}+u$
• C. $\frac{2d}{t}-u$
• D. $\frac{d}{t}$

Answer 1

The correct option is C $\frac{2d}{t}-u$

He hears the echo after t time. So the velocity of the sound to travel a distance of 2d is $=2d/t$.

Now the man is also moving towards the cliff with a velocity u so the actual velocity of the sound in the air is $=(\frac{2d}{t}-u)$ m/s