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Question

A man holds an umbrella at 30 with the vertical to keep himself dry. He then runs at a speed of 10 m/s and finds the rain drops to be hitting vertically. Speed of the rain drops w.r.t the running man and w.r.t earth are

A
20 m/s, 10 m/s
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B
10 m/s, 203 m/s
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C
103 m/s, 20 m/s
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D
20 m/s, 103 m/s
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Solution

The correct option is C 103 m/s, 20 m/s
vm= velocity of man,
vre= velocity of rain w.r.t earth
vrm= velocity of rain w.r.t man

Given: Velocity of man, vm=10 m/s
Initially, the rain is falling at 30 to the vertical


Using sin30=vmvre,
vre=vmsin30=101/2=20 m/s
Again, cos30=vrmvre
or vrm=vrecos30
vrm=20×32=103 m/s

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