A boy, who can swim at 2.5 km/h in still water, wants to swim directly across a river and land directly North of their starting point. The current in the river of 2.0 km/h [W].

Answer 1

This is a great question that has a few parts to solving.

Given:

Still water swim speed: 2.5km/h

River current speed: 2.0km/h

Since we know that the boy will be affected by the current and therefore his swim speed will be slightly less. We want to start by finding the appropriate angle he will have to swim in order to end up directly North of his current location on the South side of the river.

θ = 2.5sinθ = 2.0 ⇒ sinθ = 0.8 ⇒ ≅ 53.1°

So from his location, he will want to swim at an angle of 53.1 degrees upstream. This will help him cross the river, and the current will push him down so that he lands directly North of his starting position.

Now, we can determine how fast he will end up swimming.

Vnorth = 2.5cosθ = 2.5√(1-(0.8)²) = 2.5(0.6) = 1.5km/h

Now that we know his angle of trajectory and we know his affected swim speed, let's find out how long it will take.

t = W(km)/1.5(km/h) = h

With W being the width of the river (km), divided by the new swim speed.

So let's say the River width is 100ft = 0.03048km

0.03048/1.5 = 0.02032h = 1.2192m