   Chapter 4.4, Problem 78E ### 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

# If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is v = m g c ( 1 − e − c t / m ) where g is the acceleration due to gravity and c is a positive constant. (In Chapter 9 we will be able to deduce this equation from the assumption that the air resistance is proportional to the speed of the object; c is the proportionality constant.)(a) Calculate lim t → ∞ v . What is the meaning of this limit?(b) For fixed t, use l’Hospital’s Rule to calculate lim c → 0 + v . What can you conclude about the velocity of a falling object in a vacuum?

(a)

To determine

To calculate: The value of the limit limtv and determine its meaning.

Explanation

Given:

If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is given by following function v=mgc(1ectm), where, g is acceleration due to gravity and c is a positive constant.

Calculation:

Consider the limit,

limtv=limtmgc(1ectm)=mg

(b)

To determine

To calculate: The value of the limc0+v and determine its meaning.

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