An athlete crosses a 25-m-wide river by swimming perpendicular to the water current at a speed of 0.5 m/s relative to the water. He reaches the opposite side at a distance 40 m downstream from his starting point. How fast is the water in the river flowing with respect to the ground? What is the speed of the swimmer with respect to a friend at rest on the ground?

Solution 65PE

Step 1 of 4</p>

In the given problem, a swimmer passes a river by swimming perpendicular to the water current with width with speedrelative to water. Swimmer reaches the other end of river by covering a distance of downstream from the starting point as shown in the figure below. Here we need to calculate the speed of water in river with respect to ground and also the speed of swimmer with respect to ground.

The relative speed is the speed of an object measured from a particular reference frame and it will vary as the reference frame changes. As in the given case it varies for a swimmer relative to water and relative to ground.

Step 2 of 4</p>To calculate the speed of water relative to ground,

In order to calculate the speed of water relative to ground, first we need to calculate the time taken to swim over the river with perpendicular to water current. So that the swimmer will be swept by the water current to a distance of downstream in the time with the speed of water current.

The time taken by the swimmer to cover a width of river with a perpendicular speed relative to water as is given by,

Substituting and