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Q.Rain is falling vertically with a speed of 35m/s. A women rides a bicycle with a speed of 12 m/s in east to west direction. In which direction should she

hold her umbrella?



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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.

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