Question

A man standing on a road holds his umbrella at 30º with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/ h. He finds that rain drops are hitting his head vertically, the speed of raindrop with respect to the road will be-

(1) 10 km/h 

(2) 20 km/h

(3) 30 km/h 

(4) 40 km/h

Answer 1

Correct Answer is: (2) 20 km/h

When the man is at rest w.r.t. the ground, the rain comes to him at an angle 30º with the vertical. This is the direction of the velocity of rain drops with respect to the ground.

Here Vector v_r.g = elocity of rain with respect to the ground Vector v_m.g = velocity of the man with respect to the ground. and Vector v_r.m = velocity of the rain with respect to the man,

Taking horizontal components eq. (A) gives

v_r,g sin 30º = v_m,g = 10 km/h

or v_r,g = 10/ sin 30° = 20 km/h