Question

A boy stands in from of a cliff on the other side of a river. He fires a gun and hears an echo after 6 seconds. The boy then moves backward by 170 m and again fires the gun. He hears an echo after 7 seconds. Calculate
(i) width of river,
(ii) speed of sound.

Answer 1

Let the width of the river = x

(i) When the boy stands on the bank of the river
Now, V = `"2d"/"t"`
V = `(2"x")/6` .............(a)

(ii) When the boys move 170 m away from the bank.
Distance of boy from cliff = x + 170
Now V = `(2"x")/"t"`
Or V = `(2("x"+170))/7` .........(b)
Comapring (a) and (b)
`(2"x")/6=(2"x"+340)/7`
14x = 12x + 2040
x = 1020 m
Width of river = 1020 m.
Substituting value of x in (i)
V = `(2xx1020)/6`
V = 340 ms⁻¹.