A swimmer wants to cross a river, going from Point A to Point B, as shown in the figure above.

The distance d1 (from Point A to Point C) is 200 m. The distance d2 (from Point C to Point B) is 150 m. And the speed of the current in the river, vr, is 5 km/h to the East.

Suppose that the swimmer’s velocity relative to the water, us, makes an angle of θ = 45 degrees with the straight vertical line from Point A to Point C, as indicated in the figure.

To swim directly from Point A to Point B, what speed, us, relative to the water, should the swimmer have? (**The swimmer’s relative velocity vector, us, is shown in bottom lefthand corner of the figure.)