A swimmer wants to swim straight across a river with current flowing at a speed of v1 = 0.32 km/h. If the swimmer swims in still water with speed v2 = 0.85 km/h, at what angle θ should the swimmer point upstream from the shore and at what speed v will the swimmer swim across the river?

For the swimmer to go straight the sin component of his velocity should  cancel the river velocity.

So, we have [tex]v_{1} = v_2sin[/tex]θ

This angle θ is the angle  shall the swimmer point upstream from the shore.

0.32 = 0.85 sin[/tex]θ

θ = [tex]22.12^0[/tex]

The velocity of swimmer across the river is given by cos componet of his velocity

 v = 0.85 cosθ = 0.85 cos 22 = 0.79 m/s