(a)
To Formulate:The time needed to make a roundtripof total distance when the boat is movingupstream and back downstream.
(a)
Answer to Problem 66GP
The total time taken to cover D distance of roundtrip is
Explanation of Solution
Given data:
Speed of boat in still water is v .
The speed of river current is u .
Total distance of roundtrip is D.
Formula used:
The speed-distance relation is given by:
Where, s is the speed of an object travelling d distance in t time.
Calculation:
Assume speed of boat in still water, v is more than the speed of river current, u , otherwise the boat will not move upstream.
The distance covered when the boat moves upstream is
While moving upstream, the boat moves against the river current.
Therefore, speed of the boat,
Hence, the time taken to move upstream,
While moving downstream, the boat moves with the river current.
Therefore, speed of the boat,
The distance covered when the boat moves downstream is
Hence, the time taken to move downstream,
Therefore, total time taken to cover D distance of roundtrip is
Conclusion:
The total time taken to cover D distance of roundtrip is
(b)
To Formulate:The time needed to make a roundtripof total distance when the boat is movingdirectly across the river and back.
(b)
Answer to Problem 66GP
The totaltime needed to make a roundtripwhen the boat is movingdirectly across the river and back is
Explanation of Solution
Given data:
Speed of boat in still water is v .
The speed of river current is u .
Total distance of roundtrip is D.
Formula used:
The speed-distance relation is given by:
Where s is the speed of an object travelling d distance in t time.
Calculation:
For the boat to move directly across the water, it must at a certain angle with river current such that net velocity is straight across the river.
Assume speed of boat in still water, v is more than the speed of river current, u .
That is,
Now, the velocity of boat relative to shore,
The distance covered when the boat moves across the river is
Hence, the time taken to move directly across the river
Similarly the time taken in coming back is
Therefore, total time taken to cover D distance of roundtrip is
Conclusion:
The total time needed to make a roundtripwhen the boat is movingdirectly across the river and back is
Chapter 3 Solutions
Physics: Principles with Applications
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