Question

A man standing in front of a vertical cliff fires a gun. He hears an echo after 35s. On moving close to the cliff by 82.5 m he fires again. This time he hears the echo after 2.55s. Calculate the speed of sound, distance, and the initial position of man from the cliff.

Answer 1

Given: t = 35, d = x m

t₁ = 2.55s, d₁ = (x − 82.5)m

v = `"2d"/"t"="2x"/3`.........(i)

v = `"2d"_1/"t"_1=(2"x"-165)/2.5` .........(ii)

Comparing (i) and (ii)

`(2"x")/3=(2"x"-165)/2.5`

or 5x = 6x − 165 × 3

x = 495m

Substituting this value in (i)

v = `(2xx495)/3` = 330 m/s.