Question

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. They reach the opposite side at a distance 40 m downstream from the starting point.

(a) How fast is the water in the river flowing with respect to the ground?
(b) What is the speed of the swimmer with respect to a friend at rest on the ground?

The speed of the water in the river with respect to the ground is approximately:

a) 0.6 m/s
b) 0.8 m/s
c) 1.0 m/s
d) 1.2 m/s

Answer 1

The water in the river is flowing at a speed of approximately 0.6 m/s with respect to the ground. The swimmer's speed with respect to a friend at rest on the ground is also approximately 0.6 m/s.

Step-by-step explanation:

In this scenario, we can use the concept of relative velocity to determine the speed of the water in the river with respect to the ground.

(a) To find the speed of the water, we can consider the speed of the swimmer relative to the ground. The swimmer's speed with respect to the ground can be found by using the Pythagorean theorem. We can find the swimmer's speed relative to the ground by taking the square root of the sum of the squares of the swimmer's speed relative to the water and the speed of the water relative to the ground.

The speed of the swimmer relative to the ground is approximately 0.6 m/s.

(b) The speed of the swimmer with respect to a friend at rest on the ground can be found by subtracting the speed of the water with respect to the ground from the speed of the swimmer with respect to the ground.

The speed of the swimmer with respect to a friend at rest on the ground is also approximately 0.6 m/s.