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Question

Rain pouring down at an angle α with the vertical has a speed of 10 m/s. A girl runs against the rain with the speed of 8 m/s and sees that the rain makes an angle β with the vertical, then relation between α and β is

A
tanα=8+10sinβ10cosβ
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B
tanβ=8+10sinα10cosα
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C
tanα=tanβ
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D
tanα=cotβ
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Solution

The correct option is B tanβ=8+10sinα10cosα
As per the question, let the condition be as shown in the figure

Given, speed of rain, Vr=10 m/s
speed of girl, Vg=8 m/s
From the figure we have
tanβ=Vg+VrsinαVrcosα=8+10sinα10cosα

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