Question

A man wishes to swim across a river 0.5 km wide if he can swim at the rate of 2 km/ he in still water and the river flows at the rate of 1 km/ hr the angle made by the direction along which he should swim so as to reach a point exactly opposite to starting point should be

Answer 1

Answer:

He must swim at angle of 60° to reach the point opposite to starting point.

Explanation:

Given data:

velocity of man in still water is 2 km/hr

velocity of the river is 1 km/hr

to find: angle θ made by the direction along which she should swim to reach a point exactly opposite to starting point.

Let the river flowing in the rightward direction so the relative velocity of the man w.r.t water should be in the leftward direction and with a 2 km/hr component of upstream.

Therefore,

Relative velocity component will be = √[2² – 1²] = √3  km/hr

Since the man must swim at an angle θ so as to reach the point just opposite to the starting point relative to horizontally straight-across the river. So, we can write the equation as  

Relative velocity component along horizontal direction = (relative velocity component / velocity of the man in still water)

i.e., √3 cos θ = √3/2

or, cos θ = ½  

or, θ = cos⁻¹(1/2) = 60°