Question

Two persons A and B are standing in front of a cliff in the same line 170 m apart as shown in the diagram. Person B fires the gun and hears the echo in 3 s. Then the person A standing in front of the person B fires the gun.

(The speed of sound in air is 340 m/s.)

1. Calculate:
   1. the distance of the person B from the cliff.
   2. the minimum time in which B hears the gunshot fired by A.

Answer 1

Given: Distance between A and B = 170 m

Time taken by person B to hear the echo = 3 s

Speed of sound in air = 340 ms⁻¹

a. 1. Let the distance of person B from the cliff be d.

So,

d = `("Speed of sound in air" xx "Time taken")/2`

= `(340 xx 3)/2`

= 170 × 3

= 510 m

Hence, the distance of person B from the cliff is 510 m.

2. Person B first hears the direct sound of the gunshot and only afterwards hears its echo from the cliff. Therefore, the minimum time in which B hears the gunshot is the time taken by the sound to travel directly from person A to person B, who is 170 m away.

Then, the minimum time (t) is given by,

t = `"Distance between A and B"/"Speed of sound in air"`

= `170/340`

= 1/2`

= 0.5 s

Hence, the minimum time in which B hears the gunshot fired by A is 0.5 seconds.