Q 11-03-027NEETJEE MainMedium
Rain is falling vertically at $6$ m/s. A man runs on a level road at $8$ m/s. To protect himself, he should hold his umbrella
Answer: (D) tilted forward at $\tan^{-1}\left(\dfrac{4}{3}\right)$ with the vertical
Velocity of rain relative to the man:
$$\vec{v}_{rm} = \vec{v}_r - \vec{v}_m = 6\ \text{(down)} - 8\ \text{(forward)} = 6\ \text{down} + 8\ \text{backward}$$
The rain appears to come from in front of him, moving down and backward, so he tilts the umbrella forward. Its angle with the vertical:
$$\tan\theta = \frac{8}{6} = \frac{4}{3}$$
(The rain hits him at $10$ m/s relative to him.)
Solution by Sreeraj P, M.Sc Physics