Physics for Scientists and Engineers, Vol. 1
Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution
Check Mark

Answer to Problem 60P

The unit vector in the northeast direction is 12i^+12j^.

Explanation of Solution

Given:

Unit vectors i^ and j^ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is v=vxi^+vyj^ .

Write the expression for vector in terms of its components.

  v=vcosθi^+vsinθj^   ............... (1)

Here, v is the vector and v is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle 45° with +x axis.

Calculation:

Substitute 1 for v and 45° for θ in equation (1).

  v=1cos45°i^+1sin45°j^=12i^+12j^

Conclusion:

Thus, the unit vector in the northeast direction is 12i^+12j^.

(b)

To determine

The unit vector in 70° clockwise from y axis.

(b)

Expert Solution
Check Mark

Answer to Problem 60P

The unit vector in 70° clockwise from y axis is 32i^12j^ .

Explanation of Solution

Given:

Unit vectors i^ and j^ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is v=vxi^+vyj^ .

Write the expression for vector in terms of its components.

  v=vcosθi^+vsinθj^   ............... (1)

Here, v is the vector and v is the magnitude of vector.

When the unit vector is in 70° clockwise from y axis it will make 30° with x axis.

Calculation:

Substitute 1 for v and 30° for θ in equation (1).

  v=cos30°i^1sin30°j^=32i^12j^

Conclusion:

Thus,the unit vector in 70° clockwise from y axis. 32i^12j^.

To determine

The unit vector in the southwest direction.

Expert Solution
Check Mark

Answer to Problem 60P

The unit vector in the southwest direction is 12i^12j^ .

Explanation of Solution

Given:

Unit vectors i^ and j^ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is v=vxi^+vyj^ .

Write the expression for vector in terms of its components.

  v=vcosθi^+vsinθj^   ............... (1)

Here, v is the vector and v is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle 45° with x axis.

Calculation:

Substitute 1 for v and 45° for θ in equation (1).

  v=1cos45°i^1sin45°j^=12i^12j^

Conclusion:

Thus, the unit vector in the southwest direction is 12i^12j^.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Suppose you have a lens system that is to be used primarily for 620-nm light. What is the second thinnest coating of fluorite (calcium fluoride) that would be non-reflective for this wavelength? × nm 434
The angle between the axes of two polarizing filters is 19.0°. By how much does the second filter reduce the intensity of the light coming through the first? I = 0.106 40 x
An oil slick on water is 82.3 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength, in nanometers), given its index of refraction is 1.43? (Assume the index of refraction of water is 1.33.) wavelength color 675 × nm red (1 660 nm)
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Introduction to Vectors and Their Operations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=KBSCMTYaH1s;License: Standard YouTube License, CC-BY