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. $sin^{-1}\left(\frac{12}{35}\right)$
• B. $cos^{-1}\left(\frac{12}{35}\right)$
• C. $tan^{-1}\left(\frac{12}{35}\right)$
• D. $cot^{-1}\left(\frac{12}{35}\right)$

Answer 1

Answer: (C)

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

Answer 2

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 $\theta$ is the angle which resultant velocity $\vec{v}_{R}$ makes with the vertical, then $tan\,\theta=\frac{v_{w}}{v_{r}}=\frac{12}{35}$ or $\theta=tan^{-1}\left(\frac{12}{35}\right)$