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)...
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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.
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