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.

Options

A. `20kmh^(-1)`
B. `10sqrt(3)kmh^(-1)`
C. `20sqrt(3)kmh^(-1)`
D. `10kmh^(-1)`

Answer

A

Explanation

When the man is at rest w.r.t the ground the rain comes to him at an angle `30^(@)` with the vertical.This is the direction of the velocity of raindrops w.r.t the ground.

Here `v_(rg)=` velocity of the rain w.r.t the groud.
`v_(rm)=v_(rg)+v_(gm)=v_(rg)`
`-v_(mg)=v_(rg)+(-v_(mg))`
`v_(mg)=` velocity of the man w.r.t the ground
and `v_(rm)=` velocity of the rai w.r.t the man.
Here `v_(rg)sin 30^(@)=v_(mg)=10kmh^(-1)`
`impliesv_(rg)=10/(sin 30^(@))=20kmh^(-1)`