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Question

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 kmh1 . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

A
20 kmh1
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B
102 kmh1
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C
203 kmh1
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D
10 kmh1
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Solution

The correct option is A 20 kmh1
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, vrg= velocity of the rain w.r.t. the ground and vmg is the velocity of man w.r.t. the ground.



From figure,
sin30=|vmg||vrg|
or |vrg|=|vmg|sin30
=101/2=20 kmh1

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