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JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Kinematics

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A river of width 200 m is flowing from west to east with a speed of . A boat, moving with speed of in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are
____ and ____ respectively.
  1. (A)20 s and 100 m
  2. (B)40 s and 0 m
  3. (C)40 s and 200 m✓ Correct
  4. (D)40 s and 100 m

Answer: (C)

Solution

The boat's speed in still water is and the river's speed is . The crossing time is least when the boat is steered straight across, its velocity relative to the water pointing perpendicular to the banks, so the whole is used to cross: one crossing takes and the bank-to-bank round trip takes . During this time the stream carries the boat downstream at , so the displacement along the bank is . The minimum time is 40 s and the displacement along the bank is 200 m.

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option

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