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
Physics
![### Educational Content
#### Vector Decomposition
**Problem:**
Using the component method, decompose the following vector **A** into its components, \( A_x \) and \( A_y \).
**Diagram Explanation:**
The diagram shows a vector **A** with a magnitude of 18.0 m. It is directed at an angle of 70.0° measured counterclockwise from the positive x-axis. The coordinate system is standard, with +x to the right and +y upwards.
#### Problem 7
**Scenario:**
Colin walks 75.0° north of east for 0.800 km. Dennis, preferring to avoid diagonal paths, walks due east and then turns due north to meet Colin.
**Questions:**
- How far does Dennis walk due east?
- How far does he then walk due north?
- Verify your answer using the Pythagorean Theorem.
**Hints for Solution:**
1. Break down Colin’s path into eastward (x-direction) and northward (y-direction) components.
2. Use trigonometric functions sin(θ) and cos(θ) to find these components:
- Eastward: \( \cos(75.0°) \times 0.800 \) km
- Northward: \( \sin(75.0°) \times 0.800 \) km
3. Dennis' total path is the sum of these components.
4. Verify using the Pythagorean Theorem:
\[
\text{Total Distance} = \sqrt{(\text{Eastward Component})^2 + (\text{Northward Component})^2}
\]
This problem demonstrates vector decomposition and real-world applications of trigonometry and the Pythagorean Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8894d32-cbf3-4323-b5fb-a31877ed5631%2F4dce457a-0617-4bc3-bb62-111a4bcec3a8%2Flgcomiq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content
#### Vector Decomposition
**Problem:**
Using the component method, decompose the following vector **A** into its components, \( A_x \) and \( A_y \).
**Diagram Explanation:**
The diagram shows a vector **A** with a magnitude of 18.0 m. It is directed at an angle of 70.0° measured counterclockwise from the positive x-axis. The coordinate system is standard, with +x to the right and +y upwards.
#### Problem 7
**Scenario:**
Colin walks 75.0° north of east for 0.800 km. Dennis, preferring to avoid diagonal paths, walks due east and then turns due north to meet Colin.
**Questions:**
- How far does Dennis walk due east?
- How far does he then walk due north?
- Verify your answer using the Pythagorean Theorem.
**Hints for Solution:**
1. Break down Colin’s path into eastward (x-direction) and northward (y-direction) components.
2. Use trigonometric functions sin(θ) and cos(θ) to find these components:
- Eastward: \( \cos(75.0°) \times 0.800 \) km
- Northward: \( \sin(75.0°) \times 0.800 \) km
3. Dennis' total path is the sum of these components.
4. Verify using the Pythagorean Theorem:
\[
\text{Total Distance} = \sqrt{(\text{Eastward Component})^2 + (\text{Northward Component})^2}
\]
This problem demonstrates vector decomposition and real-world applications of trigonometry and the Pythagorean Theorem.
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