College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
Find the magnitudes of velocities vA and vB in the figure below, where,
θ = 22.0°
and
vtot = 6.92 m/s.
![### Vector Addition Diagram
#### Description:
The diagram in question illustrates vector addition in a two-dimensional coordinate system. The x and y axes are depicted to represent different directions in the plane.
#### Components:
1. **Vectors:**
- \( \mathbf{v_A} \): This vector points from the origin along a direction forming an angle of \( 26.5^\circ \) with the positive x-axis.
- \( \mathbf{v_B} \): This vector starts at the head of \( \mathbf{v_A} \) and points upwards, forming an angle of \( 23.0^\circ \) with the resultant vector \( \mathbf{v_{tot}} \).
- \( \mathbf{v_{tot}} \): The resultant vector, depicted as the vector sum \( \mathbf{v_A} + \mathbf{v_B} \). It starts from the origin and ends at the head of \( \mathbf{v_B} \). It forms an angle \( \theta \) with the positive x-axis.
2. **Angles:**
- \( 26.5^\circ \): The angle between \( \mathbf{v_A} \) and the positive x-axis.
- \( 23.0^\circ \): The angle between \( \mathbf{v_B} \) and \( \mathbf{v_{tot}} \).
#### Mathematical Representation:
The overall vector relationship can be summarized as:
\[ \mathbf{v_{tot}} = \mathbf{v_A} + \mathbf{v_B} \]
This diagram is essential in understanding the graphical method of vector addition where vectors are placed tip-to-tail to determine the resultant vector.
#### Applications:
This representation is useful in many fields including physics, engineering, and computer science, where vector addition is fundamental in analyzing forces, velocities, and other directional quantities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F086bbff5-cebe-457b-a380-688dda6bddc1%2Faff99b88-fae2-417c-bf08-49766f62bb13%2Fkht2uz.png&w=3840&q=75)
Transcribed Image Text:### Vector Addition Diagram
#### Description:
The diagram in question illustrates vector addition in a two-dimensional coordinate system. The x and y axes are depicted to represent different directions in the plane.
#### Components:
1. **Vectors:**
- \( \mathbf{v_A} \): This vector points from the origin along a direction forming an angle of \( 26.5^\circ \) with the positive x-axis.
- \( \mathbf{v_B} \): This vector starts at the head of \( \mathbf{v_A} \) and points upwards, forming an angle of \( 23.0^\circ \) with the resultant vector \( \mathbf{v_{tot}} \).
- \( \mathbf{v_{tot}} \): The resultant vector, depicted as the vector sum \( \mathbf{v_A} + \mathbf{v_B} \). It starts from the origin and ends at the head of \( \mathbf{v_B} \). It forms an angle \( \theta \) with the positive x-axis.
2. **Angles:**
- \( 26.5^\circ \): The angle between \( \mathbf{v_A} \) and the positive x-axis.
- \( 23.0^\circ \): The angle between \( \mathbf{v_B} \) and \( \mathbf{v_{tot}} \).
#### Mathematical Representation:
The overall vector relationship can be summarized as:
\[ \mathbf{v_{tot}} = \mathbf{v_A} + \mathbf{v_B} \]
This diagram is essential in understanding the graphical method of vector addition where vectors are placed tip-to-tail to determine the resultant vector.
#### Applications:
This representation is useful in many fields including physics, engineering, and computer science, where vector addition is fundamental in analyzing forces, velocities, and other directional quantities.
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 now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
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.Recommended textbooks for you
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
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