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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![### Challenge Question:
By following the triangle method or parallelogram method, graphically add the following two vectors:
\[ \vec{V_1} \] (represented as a horizontal arrow pointing to the right)
\[ + \]
\[ \vec{V_2} \] (represented as an upward arrow oriented at an angle)
\[ = \]
### Explanation for the Diagram:
You are given two vectors, \(\vec{V_1}\) and \(\vec{V_2}\).
- \(\vec{V_1}\) is depicted as a horizontal arrow pointing to the right.
- \(\vec{V_2}\) is depicted as an arrow pointing upwards at an angle.
### Methods to Graphically Add Vectors:
#### 1. Triangle Method (Head-to-Tail Method):
1. Draw \(\vec{V_1}\) as given.
2. From the head (tip) of \(\vec{V_1}\), draw \(\vec{V_2}\) maintaining its magnitude and direction.
3. The resultant vector, \(\vec{R}\), is drawn from the tail of \(\vec{V_1}\) to the head of \(\vec{V_2}\).
#### 2. Parallelogram Method:
1. Draw \(\vec{V_1}\) and \(\vec{V_2}\) starting from the same initial point.
2. Complete the parallelogram using \(\vec{V_1}\) and \(\vec{V_2}\) as adjacent sides.
3. The resultant vector, \(\vec{R}\), is drawn from the initial point (common tail of \(\vec{V_1}\) and \(\vec{V_2}\)) to the opposite corner of the parallelogram.
These methods provide a graphical way to calculate the vector sum \(\vec{V_1} + \vec{V_2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31ef78ad-c7e0-4b44-ac55-bcc830c00299%2Fddae1778-934f-4d45-b531-8520e300896a%2Fjjf35iq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Challenge Question:
By following the triangle method or parallelogram method, graphically add the following two vectors:
\[ \vec{V_1} \] (represented as a horizontal arrow pointing to the right)
\[ + \]
\[ \vec{V_2} \] (represented as an upward arrow oriented at an angle)
\[ = \]
### Explanation for the Diagram:
You are given two vectors, \(\vec{V_1}\) and \(\vec{V_2}\).
- \(\vec{V_1}\) is depicted as a horizontal arrow pointing to the right.
- \(\vec{V_2}\) is depicted as an arrow pointing upwards at an angle.
### Methods to Graphically Add Vectors:
#### 1. Triangle Method (Head-to-Tail Method):
1. Draw \(\vec{V_1}\) as given.
2. From the head (tip) of \(\vec{V_1}\), draw \(\vec{V_2}\) maintaining its magnitude and direction.
3. The resultant vector, \(\vec{R}\), is drawn from the tail of \(\vec{V_1}\) to the head of \(\vec{V_2}\).
#### 2. Parallelogram Method:
1. Draw \(\vec{V_1}\) and \(\vec{V_2}\) starting from the same initial point.
2. Complete the parallelogram using \(\vec{V_1}\) and \(\vec{V_2}\) as adjacent sides.
3. The resultant vector, \(\vec{R}\), is drawn from the initial point (common tail of \(\vec{V_1}\) and \(\vec{V_2}\)) to the opposite corner of the parallelogram.
These methods provide a graphical way to calculate the vector sum \(\vec{V_1} + \vec{V_2}\).
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