JEE Main 2026 — Jan 21, Shift 2 — Physics solution

JEE Main2026Jan 21, Shift 2Physics

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.

A
20 s and 100 m
B
40 s and 0 m
C
40 s and 200 m
D
40 s and 100 m

Solution

Convert speeds: river $v_{R} = 18$ km/h $= 5$ m/s; boat $v_{B} = 36$ km/h $= 10$ m/s.

Minimum-time crossing requires the boat's velocity to point straight across the river (perpendicular to flow). Crossing speed across river $= 10$ m/s. Time across $= 200/10 = 20$ s. Round trip (across and back) $= 40$ s.

During those 40 s, the river drags the boat along the bank by $v_{R} \times t = 5 \times 40 = 200$ m. So net displacement along the bank is 200 m.

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