   Chapter 2.6, Problem 69E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# In Chapter 9 we will be able to show, under certain assumptions, that the velocity v(t) of a falling raindrop at time t is v ( t ) = v * ( 1 − e − g t / v * ) where g is the acceleration due to gravity and v* is the terminal velocity of the raindrop.(a) Find lim t → ∞ v ( t ) . (b) Graph v(t) if v* = 1 m/s and g = 9.8 m/s2. How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity?

(a)

To determine

To find: The value of limtv(t).

Explanation

Proof:

Consider v(t)=v*(1egtv*).

Take limit of v(t) as t approaches infinity.

limtv(t)=limtv*(1egtv*)

The value of ex approaches zero as x approaches negative infinity

(b)

To determine

To find: The time taken to reach 99% of its terminal velocity.

### 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

#### The difference between population variance and sample variance.

Statistics for The Behavioral Sciences (MindTap Course List)

#### For f(x)=xx+1,f(x)=. a) 1 b) x2(x+1)2 c) 1(x+1)2 d) 1(x+1)2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Which curve is simple but not closed?

Study Guide for Stewart's Multivariable Calculus, 8th

#### Solve 34E+(18E)=214E+12 .

Mathematics For Machine Technology

#### Explain the role of voluntary participation in informed consent.

Research Methods for the Behavioral Sciences (MindTap Course List) 