   Chapter 3, Problem 30P

Chapter
Section
Textbook Problem

This is a symbolic version of Problem 29. 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 the answer in terms of d, v, and vs. (b) Using the same variables, how much time tdown does it take to swim back downstream to the starting point? (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 t a  =  2 d / v 1 -  v s 2 / v 2 (d) How much time tb does the trip take in still water?(e) Which is larger, ta or tb? Is it always larger?

(a)

To determine
The time taken for the student to swim upstream.

Explanation

The speed of the student relative to the shore while swimming upstream is,

vup=vvs

Here,

v is the speed in still water

vs is the steady speed of the river

The speed of the student relative to the shore while swimming upstream is,

vup=v+vs

Conclusion:

The time required to travel distance d upstream is,

(b)

To determine
The time taken for the student to swim downstream.

(c)

To determine
The time taken for the whole trip.

(d)

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

(e)

To determine
Which of the time is larger, ta or tb .

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 