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A current in a river flows downstream at a speed of 2 m/s. A swimmer can swin with a speed of 0.5 m/s with respect to the water. The swimmer heads directly across the stream, and crosses the stream in a time of 30 seconds.

How wide is the stream?

User Webwesen
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Final answer:

The width of the stream is 15 meters, calculated by multiplying the swimmer's velocity perpendicular to the current by the time taken to cross the stream (0.5 m/s × 30 s).

Step-by-step explanation:

The student is asking about a river crossing problem, which is a classic physics question that involves relative motion and vectors. In the scenario given, the river flows downstream at a speed of 2 m/s, and the swimmer can swim at a speed of 0.5 m/s with respect to the water. The swimmer is heading directly across the stream and crosses it in 30 seconds.

To determine how wide the stream is, we use the solution for time, width, and velocity in perpendicular motion. Since the swimmer swims directly across (perpendicular to the stream), their velocity relative to the bank of the stream is purely horizontal. Therefore, the width of the stream can be calculated using the swimmer's velocity and crossing time:

  • Width = Speed of swimmer × time crossing the stream
  • Width = 0.5 m/s × 30 s
  • Width = 15 meters

Therefore, the stream is 15 meters wide.

User Wesley Rice
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