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.

Solution

Physics sir · 4 steps

For the least time, point the boat straight across both ways, and let the river carry it east each time.

1. Convert speeds. Boat in still water: 36 km/h = 10 m s⁻¹. River: 18 km/h = 5 m s⁻¹.
2. Minimum time. Only the velocity component perpendicular to the banks moves the boat across. It is largest, 10 m s⁻¹, when the boat heads straight across. One crossing then takes 200/10 = 20 s, so the round trip takes 40 s.

   x_(drift) = vᵣ × t = 5 × 20 = 100 m per crossing

3. Drift adds up. The river flows east on both crossings, so the boat drifts 100 m east going and another 100 m east returning. The two drifts add and do not cancel, giving 200 m.
4. So. The minimum time is 40 s and the displacement along the bank is 200 m, which is option (c).

The idea to keep. Minimum time means heading perpendicular to the flow, so t = d/v_b. The river pushes the boat the same way on every crossing, so the drift on each crossing adds up.

Answer from the NTA final answer key. Solution by PrepWiser.