   Chapter 3, Problem 29P

Chapter
Section
Textbook Problem

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?

(a)

To determine
The time taken for the trip.

Explanation

The relation between the velocity of the student relative to the water, the velocity of the student relative to Earth and the water relative to Earth is,

vSW=vSEvWE

Here,

vSE is the velocity of the student relative to the Earth

vWE is the velocity of the water relative to the Earth

vSW is the velocity of the student relative to the water

If downstream is the positive direction,

vWE=0.500m/s

vSW=1.20m/s when the student is going upstream.

vSW=1.20m/s when the student is going downstream.

The velocity of the student relative to Earth going upstream is,

(vSE)upstream=vWE+(vSW)upstream

Substitute 0.500m/s for vWE and 1.20m/s for (vSW)upstream .

(vSE)upstream=0.500m/s+(1.20m/s)=0.700m/s

The distance for one leg of the trip is, 1.00km .

The time taken for the upstream journey is,

tupstream=d(vSE)upstream

Here,

d is the distance travelled

Substitute 1.00km for d and 0.700m/s for (vSE)upstream .

tupstream=(1.00km)(103m1km)0.700m/s=1

(b)

To determine
The time required for the trip in still water.

(c)

To determine
Why does the swim takes longer where there is a current.

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