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Challenge question: By following triangle method or parallelogram method to graphically add the following two vectors up: %3D 1

Challenge question: By following triangle method or parallelogram method to graphically add the following two vectors up: %3D 1

College Physics
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 \(\vec{V_1} + \vec{V_2}\).
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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