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To a man in car which is moving due east with a speed of $20 m s^{- 1},$ the rain appears to fall at an angle of $30^{0}$ with vertical. When he reduces the speed to $8 m s^{- 1}$ again the rain appears to fall at the same angle with vertical. Find the velocity of rain.

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$\sqrt{189} m s^{- 1}$

$\sqrt{304} m s^{- 1}$

$\sqrt{176} m s^{- 1}$

$\sqrt{257} m s^{- 1}$

answer is B.

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Detailed Solution

let V_x =x, V_y=y

$\tan 30^{0} = \frac{20 - x}{y}$

$\tan 30^{0} = \frac{x - 8}{y}$

20-x=x-8

$2 x = 28 \Rightarrow x = 14$ and $y = 6 \sqrt{3}$

$∴ V_{R} = \sqrt{196 + 108}$

$= \sqrt{304} m s^{- 1}$

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