Your friend Adrian is 5 ft from you—call Adrian’s position vector from you " vector A"⃑. Your friend Becky is 3 ft from Adrian—call Becky’s position vector from Adrian " Vector B".
Your friend Adrian is 5 ft from you—call Adrian’s position vector from you " vector A"⃑. Your friend Becky is 3 ft from Adrian—call Becky’s position vector from Adrian " Vector B".
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
Your friend Adrian is 5 ft from you—call Adrian’s position vector from you " vector A"⃑. Your friend Becky is 3 ft from Adrian—call Becky’s position vector from Adrian "
Vector B".
*First image is questioned, and the second image(my solution) is my professor's feedback. 1-c please write your solution in as detail as possible.
![### Problem 1:
#### Context:
- **Adrian** is 5 ft from you, noted as position vector \( \vec{A} \).
- **Becky** is 3 ft from Adrian, noted as position vector \( \vec{B} \).
- Define positions relative to reference points \( P, Q, \) and \( R \).
#### Questions:
**a.** For the **farthest distance** Becky can be from you, based on vectors, with details on angle:
- **Distance Calculations**:
\[
|\vec{R}| = 8 \text{ ft}
\]
- **Vector Sketch**: \( \vec{A} \) starts from \( P \) to \( Q \), and \( \vec{B} \) from \( Q \) to \( R \).
- **Angle**:
\[
\theta = 0^\circ
\]
**b.** For the **shortest distance** Becky can be from you:
- **Distance Calculations**:
\[
|\vec{R}| = 2 \text{ ft}
\]
- **Vector Sketch**: \( \vec{A} \) from \( P \) to \( Q \), \( \vec{B} \) from \( Q \) to \( R \).
- **Angle**:
\[
\theta = 180^\circ
\]
**c.** If Becky and Adrian are at **equal distances** from you:
- **Distance Calculations**:
\[
|\vec{R}| = 5\sqrt{2} \text{ ft}
\]
- **Vector Sketch**: Showing positions \( P, R, Q \).
- **Angle**:
\[
\theta = \cos^{-1}\left(\frac{-3}{10}\right)
\]
#### Calculations:
- Reviews and verifies using vector algebra without approximations.
- Ensures validity of shortest and longest paths through calculations.
### Additional Notes:
Corrections after problem-solving discussions were conducted and suggestions were provided:
- **Concern Regarding Angles**: Highlighted consideration of analysis-related angles.
- **Formula Errors**: Identified and recommended checking the used formulas.
This analysis is intended to assist in understanding vector positioning and calculating distances and angles in two-dimensional space through theoretical scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54957ca0-36d5-4278-b202-6dee07a291c4%2Fd71c26f6-ef9a-49f5-898d-5f6139c80e1f%2Fha4usko_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 1:
#### Context:
- **Adrian** is 5 ft from you, noted as position vector \( \vec{A} \).
- **Becky** is 3 ft from Adrian, noted as position vector \( \vec{B} \).
- Define positions relative to reference points \( P, Q, \) and \( R \).
#### Questions:
**a.** For the **farthest distance** Becky can be from you, based on vectors, with details on angle:
- **Distance Calculations**:
\[
|\vec{R}| = 8 \text{ ft}
\]
- **Vector Sketch**: \( \vec{A} \) starts from \( P \) to \( Q \), and \( \vec{B} \) from \( Q \) to \( R \).
- **Angle**:
\[
\theta = 0^\circ
\]
**b.** For the **shortest distance** Becky can be from you:
- **Distance Calculations**:
\[
|\vec{R}| = 2 \text{ ft}
\]
- **Vector Sketch**: \( \vec{A} \) from \( P \) to \( Q \), \( \vec{B} \) from \( Q \) to \( R \).
- **Angle**:
\[
\theta = 180^\circ
\]
**c.** If Becky and Adrian are at **equal distances** from you:
- **Distance Calculations**:
\[
|\vec{R}| = 5\sqrt{2} \text{ ft}
\]
- **Vector Sketch**: Showing positions \( P, R, Q \).
- **Angle**:
\[
\theta = \cos^{-1}\left(\frac{-3}{10}\right)
\]
#### Calculations:
- Reviews and verifies using vector algebra without approximations.
- Ensures validity of shortest and longest paths through calculations.
### Additional Notes:
Corrections after problem-solving discussions were conducted and suggestions were provided:
- **Concern Regarding Angles**: Highlighted consideration of analysis-related angles.
- **Formula Errors**: Identified and recommended checking the used formulas.
This analysis is intended to assist in understanding vector positioning and calculating distances and angles in two-dimensional space through theoretical scenarios.
![Here is a transcription and description suitable for an educational website:
---
**Problem 1: Vector Analysis with Friends**
You have two friends, Adrian and Becky. Consider the following scenarios based on their positions relative to you:
- **Adrian's Position**: Adrian is 5 feet away from you. Represent this with the position vector \(\vec{A}\).
- **Becky's Position**: Becky is 3 feet away from Adrian. Represent this with the position vector \(\vec{B}\) from Adrian to Becky.
### a. Farthest Distance Scenario
Determine the farthest distance Becky could be from you. Sketch the vectors in this situation:
- **Distance**: [Your answer here]
- **Sketch**: [Insert sketch showing \(\vec{A}\) and \(\vec{B}\) vectors, with Becky positioned such that the vectors form a straight line, maximizing distance.]
- **Angle**: [Your answer here, angle \(\vec{A}\) and \(\vec{B}\) in this configuration is 0 degrees.]
### b. Shortest Distance Scenario
Determine the shortest distance Becky could be from you. Sketch the vectors in this situation:
- **Distance**: [Your answer here]
- **Sketch**: [Insert sketch showing \(\vec{A}\) and \(\vec{B}\) vectors with Becky positioned such that they form a straight line in the opposite direction, minimizing distance.]
- **Angle**: [Your answer here, angle \(\vec{A}\) and \(\vec{B}\) in this configuration is 180 degrees.]
### c. Equal Distance Scenario
If Becky is the same distance from you as Adrian is, sketch the vectors:
- **Distance**: [Your calculations and answer here]
- **Sketch**: [Insert sketch showing vectors \(\vec{A}\) and \(\vec{B}\) where Becky is at a 90-degree angle from Adrian, forming an isosceles triangle with the line from you to Becky.]
- **Angle**: [Your answer here, angle is 90 degrees.]
**Instructions:**
Show detailed calculations for part (c), aiming for exact answers without approximations or calculators.
---
This setup ensures clarity in understanding the geometric and vector relationships present in the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54957ca0-36d5-4278-b202-6dee07a291c4%2Fd71c26f6-ef9a-49f5-898d-5f6139c80e1f%2F48n7fe_processed.png&w=3840&q=75)
Transcribed Image Text:Here is a transcription and description suitable for an educational website:
---
**Problem 1: Vector Analysis with Friends**
You have two friends, Adrian and Becky. Consider the following scenarios based on their positions relative to you:
- **Adrian's Position**: Adrian is 5 feet away from you. Represent this with the position vector \(\vec{A}\).
- **Becky's Position**: Becky is 3 feet away from Adrian. Represent this with the position vector \(\vec{B}\) from Adrian to Becky.
### a. Farthest Distance Scenario
Determine the farthest distance Becky could be from you. Sketch the vectors in this situation:
- **Distance**: [Your answer here]
- **Sketch**: [Insert sketch showing \(\vec{A}\) and \(\vec{B}\) vectors, with Becky positioned such that the vectors form a straight line, maximizing distance.]
- **Angle**: [Your answer here, angle \(\vec{A}\) and \(\vec{B}\) in this configuration is 0 degrees.]
### b. Shortest Distance Scenario
Determine the shortest distance Becky could be from you. Sketch the vectors in this situation:
- **Distance**: [Your answer here]
- **Sketch**: [Insert sketch showing \(\vec{A}\) and \(\vec{B}\) vectors with Becky positioned such that they form a straight line in the opposite direction, minimizing distance.]
- **Angle**: [Your answer here, angle \(\vec{A}\) and \(\vec{B}\) in this configuration is 180 degrees.]
### c. Equal Distance Scenario
If Becky is the same distance from you as Adrian is, sketch the vectors:
- **Distance**: [Your calculations and answer here]
- **Sketch**: [Insert sketch showing vectors \(\vec{A}\) and \(\vec{B}\) where Becky is at a 90-degree angle from Adrian, forming an isosceles triangle with the line from you to Becky.]
- **Angle**: [Your answer here, angle is 90 degrees.]
**Instructions:**
Show detailed calculations for part (c), aiming for exact answers without approximations or calculators.
---
This setup ensures clarity in understanding the geometric and vector relationships present in the problem.
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