Asked Dec 17, 2019

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?


Expert Answer

Step 1

Let vs be the students speed in still water, vw be the speed of water, s be the distance travelled, t1 be the time taken for the trip if the water has current, and t2 be the time taken for the trip if the water is still.

Write the expression for the time taken in the first case when the water is having a current.


Image Transcriptionclose

t V -v +v. 1m 1m (1.2 m/s – 0.5 m/s) (1.2 m/s +0.5 m/s) =1.428 s+0.588 s = 2.016 s

Step 2

Write the expression for the time taken in th...


Image Transcriptionclose

t, V. Vs 2s V. 2(1 m) (1.2 m/s) = 1.667 s


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