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Question

Rain is falling vertically with a speed of 30 ms−1. A woman rides a bicyle with a speed of 12 ms−1 in east to west direction. What is the direction in which she should hold her umbrella?

A
At an angle of tan1(25) with the vertical towards the east.
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B
At angle of tan1(25) with the vertical towards the west.
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C
At angle of tan1(25) with the vertical towards the east.
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D
At angle of tan1(25) with the vertical towards the west.
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Solution

The correct option is D At angle of tan1(25) with the vertical towards the west.

In figure, vr represents the velocity of rain and vb, the velocity of the bicycle that the woman is riding. To protect herself from rain, the woman should hold her umbrella in the direction of relative velocity of rain with respect to the bicycle, vrb.

From figure,
tanθ=vbvr=1230=25
or
θ=tan1(25)
Therefore, the woman should hold her umbrella at an angle of tan1(25) with the vertical towards the west.

Hence, option (D) is the right choice.

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