Rain is falling vertically with a speed of $35 m s^{- 1}$ . Winds starts blowing after sometime with a speed of $12 m s^{- 1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

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$\sin^{- 1} (\frac{12}{35})$

$\cos^{- 1} (\frac{12}{35})$

$\tan^{- 1} (\frac{12}{35})$

$\cot^{- 1} (\frac{12}{35})$

answer is C.

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Detailed Solution

Rain is falling vertically with a speed of 35 ms^(-1). Winds start

The velocity of the rain and the wind are represented by the vectors ${\vec{v}}_{r}$ and ${\vec{v}}_{w}$ as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity ${\vec{v}}_{R}$ . If $θ$ is the angle which resultant velocity ${\vec{v}}_{R}$ makes with the vertical, then $\tan θ = \frac{v_{w}}{v_{r}} = \frac{12}{35}$ or $θ = \tan^{- 1} (\frac{12}{35})$