Relative Velocity Of Rain
Rain falls vertically at 4 m/s while a man walks horizontally at 3 m/s on level ground, at what angle from the vertical must he tilt his umbrella?
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- relative velocity of rain
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
37 degrees
Drawing on NCERT Class 11, Chapter 4 (Motion in a Plane), the umbrella must be held along the direction of rain relative to the man, which is found by vector subtraction of the man's velocity from the rain's velocity. Relative to the man, the rain has a vertical component of 4 m/s downward and a horizontal component of 3 m/s directed opposite to his motion. The angle θ from the vertical satisfies tanθ = horizontal/vertical = 3/4, giving θ = tan⁻¹(0.75) ≈ 37°. The option 53 degrees is the complementary angle measured from the horizontal, not the vertical as asked. The option 45 degrees would require equal components of 4 m/s each, which is not the case. The option 30 degrees corresponds to tanθ = 1/√3, inconsistent with the 3:4 ratio. Plausibility check: since the horizontal component (3) is smaller than the vertical (4), the tilt should be less than 45°, and 37° correctly lies below 45°, confirming the geometry.
This hard difficulty physics question is from the chapter kinematics, covering the topic of relative velocity of rain. It appeared in the 2025 exam.
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