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JEE Main202621 January 2026Evening ShiftPhysicsMotion in Two DimensionsActual

A river of width 200 m is flowing from west to east with a speed of 18 ~km / h . A boat, moving with speed of 36 ~km / h 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.

Options

  1. A20 s and 100 m
  2. B40 s and 0 m
  3. C40 s and 200 m
  4. D40 s and 100 m

Correct answer

C. 40 s and 200 m

Step-by-step solution

Width of the river d = 200 m. Speed of river v_r = 18 km/h = 18 5 18 = 5 m/s. Speed of boat in still water v_b = 36 km/h = 36 5 18 = 10 m/s. For minimum time to cross the river, the boat must head perpendicular to the river flow (at 90^ to the bank). Time taken to cross once t = d v_b = 200 10 = 20 s. For a round trip (bank to bank and back), the total minimum time is T = 2t = 2 20 = 40 s. During the first crossing, the drift (displacement along the bank) is x₁ = v_r t = 5 20 = 100 m. During the return trip, to min

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