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A man standing on a road has to hold his...

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.

A

`10 sqrt(3)kmh^(-1)`

B

`20 kmh^(-1)`

C

`(20)/(sqrt(3))kmh^(-1)`

D

`(10)/(sqrt(3))kmh^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Velocity of rain is at `30^(@)` in vertical direction. So, its horizontal component is `upsilon_(R ) sin 30^(@)=(upsilon_(R ))/(2)`. When mamn starts walking with `10 kmh^(-1)` rain appears vertical. So horizontal component `(upsilon_(R ))/(2)` is balanced by his speed of `10 kmh^(-1)`. Thus, `(upsilon_(R ))/(2)=10` or `upsilon_(R )=20 kmh^(-1)`
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