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Rain is falling vertically with a velocity of $25 m s^{- 1} .$ A woman rides a bicycle with a speed $10 m s^{- 1}$ in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to be safe herself from rain?

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$\tan^{- 1} (0.4)$

$\tan^{- 1} (1)$

$\tan^{- 1} (\sqrt{3})$

$\tan^{- 1} (2.6)$

answer is A.

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Detailed Solution

Here, $v_{R} = 25 m s^{- 1}, v_{w} = 10 m s^{- 1}$
Velocity of rain w.r.t woman: $v_{R / W} = v_{R} - v_{W}$
Let $v_{R / W}$ make an angle $θ$ with vertical. Then $\tan θ = \frac{v_{W}}{v_{R}} = \frac{10}{2.5} = 0.4$

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