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 10kmh−1 . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is
A
20kmh−1
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B
10√2kmh−1
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C
20√3kmh−1
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D
10kmh−1
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Solution
The correct option is A20kmh−1 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=20kmh−1