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Q.

Rain, pouring down at an angle $α$ with the vertical has a speed of 10ms^-1. A girl runs against the rain with a speed of 8ms^-1 and sees that the rain makes an angle $β$ with the vertical, then relation between $α$ and $β$ is

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a

$\tan β = \frac{8 + 10 \sin α}{10 \cos α}$

b

$\tan α = \tan β$

c

$\tan α = \frac{8 + 10 \sin β}{10 \cos β}$

d

$\tan α = c o t β$

answer is B.

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Detailed Solution

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$\sin α = \frac{x}{V_{R}}; x = V_{R} \sin α$

$\cos α = \frac{y}{V_{R}}; y = V_{R} \cos α; Tan β = \frac{x + V_{G}}{y}$

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Rain, pouring down at an angle α with the vertical has a speed of 10ms-1. A girl runs against the rain with a speed of 8ms-1 and sees that the rain makes an angle βwith the vertical, then relation between α and β is