Question

15. A swimmer crosses a river in shortest distance. Ifhe tries to swim at 4 km/hr maintaining 120° withthe downstream then speed of the river is(1) 1 km/hr(2) 2 km/hr(3) 3 km/hr(4) 4 km/hr​

Answer 1

answer : option (2) 2 Km/hr

explanation : A swimmer crosses a river in shortest distance. in figure, it is clear that swimmer have to go along BA. (perpendicular line is the shortest distance between two parallel lines. )

it is given that, swimmer tries to swim at 4km/hr maintaining 120° with the downstream.

so, angle between swimmer and AB line = 30°

so, component of velocity of swimmer along BA , Vs cos30° = (4km/hr)cos30° = 2√3 km/hr

component of swimmer along horizontal direction , Vs sin30° = 4sin30° = 2 km/hr

but velocity along horizontal direction should be zero.

so, velocity of swimmer in horizontal direction = velocity of river

i.e., Vs sin30° = Vr [ see figure ]

or, 2 km/hr = Vr

hence, speed of of river = 2 km/hr