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
B
tanβ=8+10sinα10cosα
C
tanα=tanβ
D
tanα=cotβ

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 $$\beta = \dfrac{(8 + 10 sin \alpha) }{ 10 cos\alpha}$$ Physics

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