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Question

Rain pouring down at an angle $$\alpha$$ with the vertical has a speed of $$10  ms^{-1}$$. A girl runs against the rain with a speed of $$8  ms^{-1}$$ and sees that the rain makes an angle $$\beta$$ with the vertical. The relation between $$\alpha$$ and $$\beta$$ 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 $$\displaystyle \tan\beta=\frac{8+10\sin\alpha}{10\cos\alpha}$$
See the diagram,
When the girl moves in direction opposite to rain, due to relative concept, the observed horizontal component of rain increases by 8.
Therefore,
tan $$\beta = \dfrac{(8 + 10 sin \alpha) }{ 10 cos\alpha}$$ 
90534_29399_ans.png

Physics

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