A man holds an umbrella at 30∘ with the vertical to keep himself dry. He then runs at a speed of 10m/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
20m/s, 10m/s
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B
10m/s, 20√3m/s
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C
10√3m/s, 20m/s
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D
20m/s, 10√3m/s
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Solution
The correct option is C10√3m/s, 20m/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=10m/s
Initially, the rain is falling at 30∘ to the vertical
Using sin30∘=vmvre, vre=vmsin30∘=101/2=20m/s
Again, cos30∘=vrmvre
or vrm=vrecos30∘ ⇒vrm=20×√32=10√3m/s