Question

A river has a steady speed of 0.461 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point.

(a) If the student can swim at a speed of 1.29 m/s in still water, how long does the trip take?
(b) How much time is required in still water for the same length swim?
(c) Intuitively, why does the swim take longer when there is a current?

Answer 1

The time it takes for the trip depends on the student's swimming speed and the speed of the river. To calculate the time, we need to find the effective speed of the student when swimming both upstream and downstream. The swim takes longer when there is a current because the student has to swim against the current when going upstream.

Step-by-step explanation:

To find out how long the trip takes, we need to calculate the time it takes to swim upstream and the time it takes to swim downstream.

(a) To swim upstream, the student's effective speed will be the difference between their swimming speed and the speed of the river. So the effective speed is 1.29 m/s - 0.461 m/s = 0.829 m/s. Therefore, the time it takes to swim upstream is 1.00 km / 0.829 m/s = 1,207 seconds.

(b) To swim downstream, the student's effective speed will be the sum of their swimming speed and the speed of the river. So the effective speed is 1.29 m/s + 0.461 m/s = 1.751 m/s. Therefore, the time it takes to swim downstream is 1.00 km / 1.751 m/s = 571 seconds.

(c) The swim takes longer when there is a current because the student has to swim against the current to make progress upstream, which requires more effort and results in a slower effective speed. The student then has to swim with the current to make progress downstream, which requires less effort and results in a faster effective speed.