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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^(@)` with the vertical to keep the rain away. He throws the umbrella and starts running at 10km/hr. He finds that rain drop are hitting his head vertically. Find the speed of rain drops with respect to (a) road (b) the moving man.

A

10 km/h

B

20 km/h

C

30 km/h

D

40 km/h

Text Solution

Verified by Experts

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 rain drops with respect to the ground.
Here ` vecV_("r.g") ` = velocity of rain with respect to the ground
` vecV_("m.g") ` =velocity of the man with respect to the ground and ` vecV_("r.m") ` velocity of the rain with respect to the man,

We have ` vecV_(r.g) = vecV_(r.m) + vecV_(m.g) ` ....(A)
Taking horizontal components eq. (A) gives
`v_(r.g) sin 30^(@) = v_(m.g) = 10 `km/h
or ` v_(r,g) = (10)/(sin 30^(@)) = 20 ` km/h
Hence correct answer is (B)
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