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Question

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 12 m/s 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 an angle of tan1(25) with the vertical towards the west
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C
At an angle of tan1(52) with the vertical towards the east
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D
At an angle of tan1(52) with the vertical towards the west
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Solution

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

In figure, Vr represents the velocity of rain and Vb represents the velocity of the bicycle with which the woman is riding. To protect herself from rain, the woman should hold her umbrella in the direction of the relative velocity of rain with respect to the bicycle i.e. Vrb.
From the figure,
tanθ=|Vb||Vr|=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.

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