Rain is falling vertically with a speed of 30ms−1. A woman rides a bicyle with a speed of 12ms−1 in east to west direction. What is the direction in which she should hold her umbrella?
A
At an angle of tan−1(25) with the vertical towards the east.
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B
At angle of tan−1(25) with the vertical towards the west.
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C
At angle of tan−1(25) with the vertical towards the east.
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D
At angle of tan−1(25) with the vertical towards the west.
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Solution
The correct option is D At angle of tan−1(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=tan−1(25)
Therefore, the woman should hold her umbrella at an angle of tan−1(25) with the vertical towards the west.