Question

An athlete crosses a 21 m wide river by swimming perpendicular to the water current at a speed of 0.35 m/s relative to the water. He reaches the opposite side at a distance 38 m downstream from his starting point.

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

Answer 1

The speed of the water in the river flowing with respect to the ground is 0.7 m/s. The speed of the swimmer with respect to a friend at rest on the ground is -0.2 m/s.

Step-by-step explanation:

To solve this problem, we can use the concept of relative velocity. The swimmer's velocity with respect to the ground is the vector sum of their velocity with respect to the water and the water's velocity with respect to the ground. Let's calculate:

1. To find the speed of the water in the river flowing with respect to the ground, we use the Pythagorean theorem. Let's assume the speed of the water in the river is vwg and the speed of the swimmer with respect to the water is vsw = 0.5 m/s.

Using the Pythagorean theorem, we have (vwg)2 = (vsw)2 + (vsg)2, where (vsg)2 is the speed of the swimmer with respect to the ground.

Let's substitute the given values into the equation:

(vg)2 = (0.5)2 + (vsg)2

Now we can solve for (vwg)2:

(vg)2 - (vsw)2 = (vsg)2

0.75 - 0.25 = (vsg)2

(vsg)2 = 0.5

vsg = 0.7 m/s

Therefore, the speed of the water in the river flowing with respect to the ground is 0.7 m/s.

2. To find the speed of the swimmer with respect to a friend at rest on the ground, we can subtract the velocity of the water in the river flowing with respect to the ground from the speed of the swimmer with respect to the water.

Therefore, the speed of the swimmer with respect to a friend at rest on the ground is 0.5 m/s - 0.7 m/s = -0.2 m/s.