Rain is falling vertically with a speed of 35 m/s. A woman rides a bicycle with a speed of 12 m/s in east to west direction. In what direction should she hold her umbrella?

Question

Arun · Answer

Dear Aabha

She should hold the umbrella a little inclined towards the west from the vertical.

The drops which are falling a little ahead of the current position of the woman, will fall on her, because she moves in that direction.

relative velocity of the rain drops wrt cyclist
= velocity of woman - velocity of rain

the magnitude of relative velocity the rain drops wrt woman
= √(12² + 35²) = 37 m/s

direction of relative velocity of the rain drops =
= tan⁻¹ (12/35) = 18.92 deg. from the vertical.

So the cyclist should hold the umbrella at 18.92 deg to the vertical in the forward direction.

Regards

Arun (askIITians forum expert)

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Rain is falling vertically with a speed of 35 m/s. A woman rides a bicycle with a speed of 12 m/s in east to west direction. In what direction should she hold her umbrella?

Rain is falling vertically with a speed of 35 m/s. A woman rides a bicycle with a speed of 12 m/s in east to west direction. In what direction should she hold her umbrella?

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