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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Add the vectors and determine the resultant
Vector A=22 m, north
Vector B=33 m, West
![### Vector Addition and Resultant Determination
**Exercise:**
Add the following component vectors and determine the resultant. (You might want to draw them).
- **Vector A**: 22 m, north
- **Vector B**: 33 m, west
**Options:**
1. 7.4 m, 56 degrees north of east
2. 40 m, 56 degrees west of north
3. 7.4 m, 34 degrees west of north
4. 40 m, 34 degrees west of north
**Explanation:**
To solve this problem, you can use graphical vector addition or the component method to determine the resultant vector. In graphical addition, you would draw vector A pointing north and vector B pointing west. The resultant vector will be the diagonal of the rectangle that these two vectors form, originating from the starting point of vector A and B.
However, for the component method, you need to break down each vector into its respective components and then add those components to find the resultant vector.
1. **North and South Direction**:
- Vector A: 22 m north.
- Vector B has no north/south component.
2. **East and West Direction**:
- Vector A has no east/west component.
- Vector B: 33 m west.
Once you have these components, you can determine the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometric functions.
The correct resultant will be given by:
\[ R = \sqrt{(22^2 + 33^2)} \approx 40 \, \text{m}\]
The angle the resultant makes with the north direction can be found using trigonometry:
\[ \theta = \tan^{-1}\left(\frac{33}{22}\right) \approx 56^\circ \]
Thus, the resultant vector is approximately 40 m, 56 degrees west of north, which corresponds to the second option:
- **40 m, 56 degrees west of north**
This is the solution to the problem based on the given component vectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d7d2d74-d827-467b-8d8e-9fee9720e388%2F8beaa814-68f2-412e-b90e-9b6baf737786%2Fm7nw3yi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Addition and Resultant Determination
**Exercise:**
Add the following component vectors and determine the resultant. (You might want to draw them).
- **Vector A**: 22 m, north
- **Vector B**: 33 m, west
**Options:**
1. 7.4 m, 56 degrees north of east
2. 40 m, 56 degrees west of north
3. 7.4 m, 34 degrees west of north
4. 40 m, 34 degrees west of north
**Explanation:**
To solve this problem, you can use graphical vector addition or the component method to determine the resultant vector. In graphical addition, you would draw vector A pointing north and vector B pointing west. The resultant vector will be the diagonal of the rectangle that these two vectors form, originating from the starting point of vector A and B.
However, for the component method, you need to break down each vector into its respective components and then add those components to find the resultant vector.
1. **North and South Direction**:
- Vector A: 22 m north.
- Vector B has no north/south component.
2. **East and West Direction**:
- Vector A has no east/west component.
- Vector B: 33 m west.
Once you have these components, you can determine the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometric functions.
The correct resultant will be given by:
\[ R = \sqrt{(22^2 + 33^2)} \approx 40 \, \text{m}\]
The angle the resultant makes with the north direction can be found using trigonometry:
\[ \theta = \tan^{-1}\left(\frac{33}{22}\right) \approx 56^\circ \]
Thus, the resultant vector is approximately 40 m, 56 degrees west of north, which corresponds to the second option:
- **40 m, 56 degrees west of north**
This is the solution to the problem based on the given component vectors.
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