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A man swims across a river flowing at 5 m/s. He reaches a point directly across in 5 seconds, covering a perpendicular distance of 60 m. What is his swimming speed in still water?

1. 12 m/s
2. 13 m/s
3. 5 m/s
4. 10 m/s

Correct answer: 13 m/s

Solution

The perpendicular distance is 60 m crossed in 5 s, so the effective velocity perpendicular to river = 60/5 = 12 m/s. He reaches directly across, meaning his resultant displacement is perpendicular to the river flow. His still-water velocity v_sw has components: v_sw² = (perpendicular component)² + (component cancelling river flow)². To reach directly across, the horizontal component of v_sw must cancel the river velocity of 5 m/s. So v_sw = sqrt(12² + 5²) = sqrt(144 + 25) = sqrt(169) = 13 m/s.

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