A man standing on a road has to hold his umbrella at 30^ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 ~km / h . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is :

Step-by-step solution

When the man is at rest with respect to the ground, the rain comes to him at an angle 30^ with the vertical. This is the direction of the velocity of raindrops with respect to the ground. Here, v _ r, g = velocity of the rain with respect to the ground v _ m, g = velocity of the man with respect to the ground and v _ r, m = velocity of the rain with respect to the man. We have, v _ r, g + v _ r, m + v _ m, g (i) Taking horizontal components, Eq. (i) gives v_ r, g 30^ =v_ m, g =10 ~km / h or v_ r, g = 10 30^ =20 ~km