A man standing on a road has to hold his umbrella at `30^0` with the vertical to keep the rain away. The throws the umbrella and starts running at 10 km/h. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to a. the road, b. the moving man.

Explanation

When the man is rest with respect to the groudn, the rain comes to him at an angle `30^0` with the with respect to the ground. The situation when the man runs is shwon in the ure.

Here `vecv_(r,g)=` velocity o fthe rain with respect to the ground
`vecv_(m,g)=` velocity of the man with respect to the ground and `vecv_(v,m)=` velocity of the rain with respect to the man.
`We have, `vecv_(r,g)=vec_(r,m)+vecv_(m,g)` ..........i
taking horizontal components equation i. gives `vec_(r,g) sin 30^0 =v_(m,g)=10 km/h`
or `v_(r,g)=(10 km/h)/(sin 30^0)=20 km/h`
Taking vertical components, equation `i gives
`vec_(r,g) cos 30^0=v_(r,m)`
`or, v_(r,m)= (20 km/h) sqrt3/2`
`=10 sqrt3 km/h`.