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.60°
- B.120°
- C.90°
- D.150°
Show answer and solution
Correct option: B
Solution
To cross straight (perpendicular to river banks), the swimmer's resultant velocity must be directed straight across, meaning the horizontal (along-river) component of the swimmer's velocity must cancel the river current.
If the swimmer makes angle θ with the river flow direction, the component along the river = 4cosθ. Setting this equal and opposite to the current: 4cosθ + 2 = 0 → cosθ = -1/2 → θ = 120°.
So the swimmer must swim at 120° with respect to the direction of river flow (i.e., 60° upstream from the perpendicular), giving a net velocity purely across the river.
If the swimmer makes angle θ with the river flow direction, the component along the river = 4cosθ. Setting this equal and opposite to the current: 4cosθ + 2 = 0 → cosθ = -1/2 → θ = 120°.
So the swimmer must swim at 120° with respect to the direction of river flow (i.e., 60° upstream from the perpendicular), giving a net velocity purely across the river.
[JEE Main 2019 · 9 Apr · Shift I]