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
Concept. Hold the umbrella against the rain's velocity relative to the man.
Step 1. Relative velocity. $\vec v_{rm} = 6$ down $+ 8$ backward.
Step 2. Tilt. The rain comes from the front, so tilt forward:
$$\tan\theta = \frac86 = \frac43$$
Answer. Tilted forward at $\tan^{-1}\left(\dfrac43\right)$ with the vertical (Option D).
Solution by Sreeraj P, M.Sc Physics