The stream of a river is flowing with a speed of $2 \mathrm{~km} / \mathrm{h}$. A swimmer can swim at a speed of $4 \mathrm{~km} / \mathrm{h}$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Kinematics

The stream of a river is flowing with a speed of

2 km / h

. A swimmer can swim at a speed of

4 km / h

. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

(A) $6 0^{\circ}$
(B) $9 0^{\circ}$
(C) $12 0^{\circ}$ ✓ Correct
(D) $15 0^{\circ}$

Answer: (C)

Solution

To cross straight over, the swimmer's velocity component along the current must exactly cancel the stream. If

θ

is the angle measured from the straight-across direction (the perpendicular to the flow), then

4 sin θ = 2

, so

sin θ = \frac{1}{2}

and

θ = 3 0^{\circ}

. Measured from the direction of the flow itself, the swimmer must aim at

9 0^{\circ} + 3 0^{\circ} = 12 0^{\circ}

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option

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