Relative Velocity In River Crossing
A swimmer who can swim at 4 m/s in still water heads straight across a river flowing at 3 m/s, what is the swimmer's resultant speed relative to the bank?
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- relative velocity in river crossing
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
5m/s
As described in NCERT Class 11, Chapter 4 (Motion in a Plane), when a swimmer heads directly across a river, the swimming velocity is perpendicular to the river current, so the two velocities combine as perpendicular vectors. The resultant speed relative to the bank is the vector sum: √(4² + 3²) = √(16 + 9) = √25 = 5 m/s. The option 7 m/s wrongly adds the speeds arithmetically as if they were along the same line. The option 1 m/s subtracts them, which would apply only to anti-parallel velocities. The option 3.5 m/s incorrectly averages the two speeds. Plausibility check: the resultant of two perpendicular vectors must be larger than either component but smaller than their direct sum, so it must lie between 4 and 7 m/s; the value 5 m/s correctly falls in this range and forms a classic 3-4-5 right triangle, confirming the vector addition.
This medium difficulty physics question is from the chapter kinematics, covering the topic of relative velocity in river crossing. It appeared in the 2025 exam.
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