Part 1 of 5 - Conceptualize The student swims upstream against the current. If t

Question

Part 1 of 5 - Conceptualize
The student swims upstream against the current. If the stream is flowing at the same rate or faster than the student can swim, he will never reach the 1.00-km mark, even after an infinite amount of time. If the stream is flowing at half the rate the student can swim, the trip upstream will take the same time as the complete round trip in still water. So we expect that the round trip will take longer than a round trip in still water. Since the student can swim 1.29 km in 1 000 s, we estimate that the trip will take about 2 000 s, which is about 30 minutes.
Part 2 of 5 - Categorize
The total time interval in the river is the longer time spent swimming upstream (against the current) plus the shorter time swimming downstream (with the current). For each part of the trip, we will use the basic equation t = d / v, where v is the speed of the student relative to the shore.
Part 3 of 5 - Analyze
(a) We know that Total time = time upstream plus time downstream. For the student's upstream time, we have
tup =
d
vstudent ? vstream
=
1000 m
m/s ? m/s
= s.
And for the student's downstream time, we have
tdown =
d
vstudent + vstream
=
1000 m
m/s + m/s
=
answer part 3

Explanation / Answer

Relative Velocity while going upstream = (1.29/1000) - (1.29/1000)/2 = 1.29/2000 km/s

Relative velocity while coming downstream = (1.29/1000) + (1.29/1000)/2 = 3/2*1.29/1000

time taken while going upstream = 1/(1.29/2000) = 1550.4 s

Time taken while going downstream = 1/(3/2*1.29/1000) = 516.8 s

Total time = 1550.4 + 516.8 = 2067.2 s = 34.45 minutes

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