College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![**Problem Statement:**
The components of a vector \( \mathbf{A} \) are \( A_X = 2.9 \) and \( A_Y = 5.3 \), and the components of a vector \( \mathbf{B} \) are given as \( B_X = 7.7 \) and \( B_Y = -10 \). What is the magnitude of the vector \( \mathbf{A} + \mathbf{B} \)?
**Answer Choices:**
- a. 12
- b. 11
- c. 13
- d. 10
- e. 9
**Solution Explanation:**
To find the magnitude of the vector \( \mathbf{A} + \mathbf{B} \), we first need to determine the components of this resultant vector.
Given:
\[ A_X = 2.9, \quad A_Y = 5.3 \]
\[ B_X = 7.7, \quad B_Y = -10 \]
The resultant vector \( \mathbf{R} = \mathbf{A} + \mathbf{B} \) will have components:
\[ R_X = A_X + B_X = 2.9 + 7.7 = 10.6 \]
\[ R_Y = A_Y + B_Y = 5.3 + (-10) = -4.7 \]
Now, to find the magnitude of the resultant vector \( \mathbf{R} \):
\[ \| \mathbf{R} \| = \sqrt{R_X^2 + R_Y^2} = \sqrt{10.6^2 + (-4.7)^2} \]
\[ \| \mathbf{R} \| = \sqrt{112.36 + 22.09} = \sqrt{134.45} \]
\[ \| \mathbf{R} \| \approx 11.6 \]
Therefore, the closest answer choice provided is:
\[ \boxed{11} \]](https://content.bartleby.com/qna-images/question/765f1446-f94a-48d3-b4ac-193b47a28028/71c3ae13-97c9-49f4-9f41-144f2267b1c7/6fwvuhh_processed.png)
Transcribed Image Text:**Problem Statement:**
The components of a vector \( \mathbf{A} \) are \( A_X = 2.9 \) and \( A_Y = 5.3 \), and the components of a vector \( \mathbf{B} \) are given as \( B_X = 7.7 \) and \( B_Y = -10 \). What is the magnitude of the vector \( \mathbf{A} + \mathbf{B} \)?
**Answer Choices:**
- a. 12
- b. 11
- c. 13
- d. 10
- e. 9
**Solution Explanation:**
To find the magnitude of the vector \( \mathbf{A} + \mathbf{B} \), we first need to determine the components of this resultant vector.
Given:
\[ A_X = 2.9, \quad A_Y = 5.3 \]
\[ B_X = 7.7, \quad B_Y = -10 \]
The resultant vector \( \mathbf{R} = \mathbf{A} + \mathbf{B} \) will have components:
\[ R_X = A_X + B_X = 2.9 + 7.7 = 10.6 \]
\[ R_Y = A_Y + B_Y = 5.3 + (-10) = -4.7 \]
Now, to find the magnitude of the resultant vector \( \mathbf{R} \):
\[ \| \mathbf{R} \| = \sqrt{R_X^2 + R_Y^2} = \sqrt{10.6^2 + (-4.7)^2} \]
\[ \| \mathbf{R} \| = \sqrt{112.36 + 22.09} = \sqrt{134.45} \]
\[ \| \mathbf{R} \| \approx 11.6 \]
Therefore, the closest answer choice provided is:
\[ \boxed{11} \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps
Knowledge Booster
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
- What are pseudo vectors? Why are they called axial vectors?arrow_forwardThree vectors A, B and C add together to yield zero, i.e. A + B + C = 0. The vectors A and C point in opposite directions and their magnitudes are related by the expression: A = 2C. Which one of the following conclusions is correct? A. A and B have equal magnitudes and point in opposite directions. B. B and C have equal magnitudes and point in the same direction. C. A and B point in the same direction, but A has twice the magnitude of B. OD. B and C point in the same direction, but C has twice the magnitude of B. E. A and Barrow_forwardSame question just asking two differentarrow_forward
- 13) While hiking, you travel 5.0 miles south (vector Ā), then turn and travel 4.0 miles at an angle of 30 degrees north of east (B). a) Sketch a diagram of these two displacement vectors, roughly to scale. Assume the positive x-axis is in the east direction, and the positive y-axis is in the north direction. b) You now wish to return to where you started. Determine the magnitude and direction of the displacement vector Ď you must follow. Use the method of components. As always, show all the details of your work. (Show vector D in the diagram above.) (Use clear, standard notation; show all details of your work. See PSL 3.4-5.)arrow_forwardHow would I figure out the adding and subtracting parallel vectors? how would I figure out the adding and subtracting anti-parallel vectors?arrow_forwardCan someone please help me understand this question and how to get the answer? Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum is: 1.) equal to 8.6m 2.) could be as small as 2.0m or as large as 12.0m 3.)is equal to 2m 4. or is equal to 12m. Thank you. I am really confused.arrow_forward
- Q(2) Consider the two vectors A= 31 – 2j and B = 2i – 3j. Calculate the angle between the two vectors A) 146° B) 47.7° C) 70° D) 22.6° O 1. D O 2. B O 3. C O 4. Aarrow_forwardVector A measures 1.20m and angles 30° above the x-axis in the first quadrant. Vector B extends 3.20m and is angled 30° beneath the x-axis in the fourth quadrant. a. Determine the magnitude and direction of A + Bb. Determine the magnitude and direction of A – Barrow_forwardQ14arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press 
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON