Question
Asked Sep 20, 2019
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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?

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Expert Answer

Step 1

Consider the motion of the student when the river has some speed. Let vr be the speed of the river, vs be the speed of the student, v1 be the relative speed of student with respect to the river travelling upstream, and v2 be the relative speed of the student with respect to the river travelling downstream. Let l be the distance travelled by the student.

Write the given information in the question.

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1 0.5 m/s 1 1.2 m/s 1 1 km 1000 m

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Step 2

Write the expression for the relative velocity of student with respect to the river travelling upstream and downstream.

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=(1.2 m/s)-(0.5 m/s) 0.7 m/s 121V =(1.2 m/s)(0.5 m/s) =1.7 m/s

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Step 3

Let t1 be the time taken for travelling upstream, and t2 be the time taken to tra...

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1000 m 0.7 m/s 23.8 min 1428.57 s or 1000 m 1.7 m/s = 588.23 s 9.8 min or

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