Question

Swimming at 2.00 m/s relative to still water, a swimmer heads directly across a river of width 85 m. He arrives 30 m downstream from the point directly across the river from his starting point.

What is the speed of the current in the river?

Answer 1

The speed of the water current in the river is approximately 1.15 m/s.

Step-by-step explanation:

To find the speed of the water current in the river, we need to use the concept of relative velocity. The swimmer is moving at a speed of 2.00 m/s relative to still water. However, because the current in the river also has a velocity, the actual speed of the swimmer relative to the ground will be different.

Let's assume the speed of the water current in the river is 'v' m/s. Since the swimmer is heading directly across the river, the component of the swimmer's velocity in the direction perpendicular to the river's flow will be equal to the width of the river, which is 85 m. Using the concept of relative velocity, we can set up the following equation:

2.00 m/s - v m/s = 85 m

Simplifying this equation, we find that the speed of the water current in the river is approximately 1.15 m/s.