Question

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?

• A. sin${}^{-1}$ (12 /35)
• B. cos${}^{-1}$ (12 /35 )
• C. tan${}^{-1}$(12 /35)
• D. cot${}^{-1}$ (12 /35)

Answer 1

The correct option is C tan${}^{-1}$(12 /35)

The velocity of the rain and the wind are represented by the vectors ${\overrightarrow{v}}_r$ and ${\overrightarrow{v}}_w$ as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity ${\overrightarrow{v}}_R$

If $\theta$ is the angle which resultant velocity ${\overrightarrow{v}}_R$ makes with the vertical, then tan$\theta$= $\frac{v_w}{v_r}=\frac{12}{35}$ or $\theta =ta{n}^{-1}\left(12/35\right)$