   Chapter 13.4, Problem 39E

Chapter
Section
Textbook Problem

# Find the tangential and normal components of the acceleration vector.39. r(t) = cos t i + sin t j + t k

To determine

To find: The tangential components of the acceleration vector and normal components of the acceleration vector.

Explanation

Given data:

r(t)=costi+sintj+tk

Formula used:

Write the expression for tangential component.

aT=r(t)r(t)|r(t)| (1)

Write the expression for normal component.

aN=|r(t)×r(t)||r(t)| (2)

Find r(t) .

r(t)=ddt[r(t)]

Substitute costi+sintj+tk for r(t) ,

r(t)=ddt[costi+sintj+tk]=ddt(costi)+ddt(sintj)+ddt(tk)=sinti+costj+k

Find r(t) .

r(t)=ddt[r(t)]

Substitute sinti+costj+k for r(t) ,

r(t)=ddt[sinti+costj+k]=ddt(sinti)+ddt(costj)+ddt(k)=costisintj+0k=costisintj

Find |r(t)|

### 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

#### Sketch the graph of y=2x1.

Calculus: An Applied Approach (MindTap Course List)

#### Show that sinxxif0x2.

Calculus (MindTap Course List)

#### True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th

#### The length of the curve given by x = 3t2 + 2, y = 2t3, is:

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