Concept explainers
A river has a steady speed of 0.500 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 1.20 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?
(a)
Answer to Problem 29P
Explanation of Solution
The relation between the velocity of the student relative to the water, the velocity of the student relative to Earth and the water relative to Earth is,
Here,
If downstream is the positive direction,
The velocity of the student relative to Earth going upstream is,
Substitute
The distance for one leg of the trip is,
The time taken for the upstream journey is,
Here,
Substitute
The velocity of the student relative to Earth going downstream is,
Substitute
The distance for one leg of the trip is,
The time taken for the upstream journey is,
Substitute
The total time for the trip is,
Substitute
Conclusion:
Thus, the time taken for the trip is
(b)
Answer to Problem 29P
Explanation of Solution
If the water is sill, the speed will be same for each leg.
The time for each leg is,
Substitute
Conclusion:
The total time taken is twice the time taken for one leg.
Substitute
The time taken for the trip in still water is
(c)
Answer to Problem 29P
Explanation of Solution
The time taken going downstream is a lot less compared to the time taken to go upstream the same distance. The current will slow the swimmer going up and it will aid the swimmer going along with the current.
Conclusion:
The time savings going downstream with the current is always less than the extra time required to go the same distance against the current.
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