Answer to Question #252681 in Mechanics | Relativity for Ahmad

Question

A man is riding a vehicle towards a vertical cliff with a velocity of 36 km/h. He fires a gunshot and hears its echo after 4 sec. The speed of sound in air is 320 m/s.

(i) The distance between the cliff and the position, where he shot the gun is:

A.640 m

B.680 m

C.620 m

D.660 m

Answer 1

36 km/h is 10 m/s.

The speed of sound is added to the speed of the motorcycle when the sound moves toward the cliff, reflects from the cliff and travels back:

$$t_1=d/(c+v),t_2=d/(c+v),\\ t=t_1+t_2=4\text{ s}.\\ d=t(c+v)/2=660\text{ m}.$$