Question

Two swimmers leave point A on one bank of the river to reach point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v₀ = 2.0 km/hour and the velocity v' of each swimmer with respect to water equals 2.5 km per hour.

Answer 1

Let one of the swimmer (say 1) cross the river along AB, which is obviously the shortest path. time taken to cross the river by the swimmer 1.

For the other swimmer (say 2), which follows the quickest path the time taken to cross the river.

If t3 be the time for swimmer 2 to walk the distance x to come from C to B (Fig.), then