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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 km/h. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to the ground.

A
5 km/h
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B
10 km/h
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C
102 km/h
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D
20 km/h
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Solution

The correct option is D 20 km/h
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. The situation when the man runs is shown in the figure


Vrg= velocity of rain drops with respect to ground.
Vman= velocity of man =10 km/h
Hence, cosθ=10Vrg
cos60=10Vrg
12=10Vrg
Vrg=20 km/h
Hence, velocity of rain drops with respect to the ground is 20 km/h.

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