A river has a steady speed of vs. A student swims upstream a distance d and back

Question

A river has a steady speed of vs. A student swims upstream a distance d and back to the starting point.
(a) If the student can swim at a speed of v in still water, how much time tup does it take the student to swim upstream a distance d? Express your answer in terms of d, v, and vs.



tup

=






(b) Using the same variables, how much time tdown does it takes to swim back downstream to the starting point?



tdown

=






(c) Sum the answers found in parts (a) and (b) and show that the time ta required for the whole trip can be written as


(Do this on paper. Your instructor may ask you to turn in this work.)

(d) How much time tb does the trip take in still water?



tb

=





(e) Which is larger, ta or tb?

ta tb

(f) Is it always larger?

Yes No

Explanation / Answer

SOLUTION: River has a steady speed of ,vs Width of the river,d Student can swim at a speed of, v (a) In order to swim up stream, the student must swim against the river's current. so relative speedof the student must be , v-vs thus, requireed time is, tup= d/v-vs _________________________________________________________________ _________________________________________________________________ (b) In order to swim downstream, the student must swim in the river's current direction. so relative speedof the student must be , v+vs thus, requireed time is, tup= d/v+vs _________________________________________________________________ _________________________________________________________________ (c) time required for total trip ta=(d/v-vs) +(d/v+vs) =2dv/v2-vs2 ____________________________________________________ ____________________________________________________ (d) the trip in still water takes, tb=2d/v ___________________________________________________ ___________________________________________________ (e) It is clear that, 2d/v >2dv/v2-vs2 Hence, tb>ta No, it happens only in the direction against to ' river flow

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