A river has a steady speed of 0.500 m / s. A student swims...

A river has a steady speed of $0.500 \mathrm{~m} / \mathrm{s}$. A student swims upstream a distance of $1.00 \mathrm{~km}$ and swims back to the starting point. If the student can swim at a speed of $1.20 \mathrm{~m} / \mathrm{s}$ in still water, how long does the trip take? Compare this with the time the trip would take if the water were still.

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Key Concepts

Comparison of Different Motion Conditions

This involves analyzing and contrasting the travel times under different conditions, such as when the medium is moving versus when it is still. By calculating both, one can determine the impact of the medium's flow on travel time.

Relative Velocity

This concept involves analyzing the net motion of an object when both the object and the medium in which it moves (such as a river) are in motion. In such problems, the object's effective speed relative to a fixed point is determined by the vector addition of its speed in still conditions and the medium's speed.

Effective Speed in a Current

When moving in a flowing medium, the effective speed changes depending on the direction relative to the current. For instance, moving against the current (upstream) reduces the runner’s or swimmer’s effective speed because the current subtracts from the object's own speed, whereas moving with the current (downstream) increases it by adding to the speed.

Travel Time Calculation

The time taken for any leg of a journey is calculated by dividing the distance by the effective speed during that leg. In problems where speeds vary in different directions (such as upstream and downstream), the total travel time is the sum of the times computed for each leg.

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