Part A Referring to the vectors in the figure, express the sum A +B+C in unit vector notation. (Figure 1) Express your answer using two significant figures. Enter the x and y components of the vector separated by comma. < 1 of 1> ? C 10m 25 Submit Reguest Answer 1.5 m 40 Provide Feedback 19 20 m B. 1.5 m
Part A Referring to the vectors in the figure, express the sum A +B+C in unit vector notation. (Figure 1) Express your answer using two significant figures. Enter the x and y components of the vector separated by comma. < 1 of 1> ? C 10m 25 Submit Reguest Answer 1.5 m 40 Provide Feedback 19 20 m B. 1.5 m
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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![**Educational Website Transcript**
---
### Part A
**Problem Statement:**
Referring to the vectors in the figure, express the sum \(\vec{A} + \vec{B} + \vec{C}\) in unit vector notation. (Figure 1)
Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.
**Input Box:**
\[ \fbox{\begin{minipage}{15em}\center \placeholder{Input box for entering the x and y components}\end{minipage}} \]
**Button:**
\[ \fbox{\center \text{Submit}} \]
**Additional Option:**
\[ \fbox{\text{Request Answer}} \]
**Provide Feedback:**
---
**Figure 1 - Vector Diagram Explanation:**
The diagram illustrates three vectors, \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\), each with magnitudes and directions as follows:
1. **Vector \(\vec{A}\):**
- Magnitude: 1.5 m
- Direction: 40° from the x-axis.
2. **Vector \(\vec{C}\):**
- Magnitude: 1.0 m
- Direction: 25° from the x-axis.
3. **Vector \(\vec{B}\):**
- Magnitude: 2.0 m
- Direction: 19° from the x-axis.
- Additionally, this vector is positioned 1.5 m below the x-axis.
**Axes:**
The horizontal axis is labeled as \(x\) and the vertical axis is labeled as \(y\).
---
**Instructions for Students:**
1. Break down each vector into its x and y components using trigonometric functions:
- The x-component: \( \text{Magnitude} \times \cos(\text{Angle}) \)
- The y-component: \( \text{Magnitude} \times \sin(\text{Angle}) \)
2. Sum the respective x and y components of all three vectors.
3. Enter the final x and y components of the resultant vector in the provided input box, separated by a comma.
Example Entry:
\[1.23, 4.56\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd955a64d-1d84-4c4c-a975-e65e2fa2eacb%2F68524ae8-8a16-4b28-bf66-b657192b171a%2Fzd5mhfo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcript**
---
### Part A
**Problem Statement:**
Referring to the vectors in the figure, express the sum \(\vec{A} + \vec{B} + \vec{C}\) in unit vector notation. (Figure 1)
Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.
**Input Box:**
\[ \fbox{\begin{minipage}{15em}\center \placeholder{Input box for entering the x and y components}\end{minipage}} \]
**Button:**
\[ \fbox{\center \text{Submit}} \]
**Additional Option:**
\[ \fbox{\text{Request Answer}} \]
**Provide Feedback:**
---
**Figure 1 - Vector Diagram Explanation:**
The diagram illustrates three vectors, \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\), each with magnitudes and directions as follows:
1. **Vector \(\vec{A}\):**
- Magnitude: 1.5 m
- Direction: 40° from the x-axis.
2. **Vector \(\vec{C}\):**
- Magnitude: 1.0 m
- Direction: 25° from the x-axis.
3. **Vector \(\vec{B}\):**
- Magnitude: 2.0 m
- Direction: 19° from the x-axis.
- Additionally, this vector is positioned 1.5 m below the x-axis.
**Axes:**
The horizontal axis is labeled as \(x\) and the vertical axis is labeled as \(y\).
---
**Instructions for Students:**
1. Break down each vector into its x and y components using trigonometric functions:
- The x-component: \( \text{Magnitude} \times \cos(\text{Angle}) \)
- The y-component: \( \text{Magnitude} \times \sin(\text{Angle}) \)
2. Sum the respective x and y components of all three vectors.
3. Enter the final x and y components of the resultant vector in the provided input box, separated by a comma.
Example Entry:
\[1.23, 4.56\]
---
![### Vector Addition Problem
#### Given Vectors
- \(\vec{A} = (13.1 \, \text{m}) \hat{i}\)
- \(\vec{B} = (-31.7 \, \text{m}) \hat{j}\)
### Part A
**Problem:** Find the direction of the vector \(2\vec{A} + \vec{B}\).
**Solution Step:**
1. Calculate \(\theta\)
2. Input the result in the given form below.
#### Input Form:
- **θ =** [ ] \(^\circ\) below the \(+x\)-axis
- Click **Submit**
### Part B
**Problem:** Find the magnitude of the vector \(2\vec{A} + \vec{B}\).
**Solution Step:**
1. Calculate the magnitude.
2. Input the result in the given form below.
#### Input Form:
- **|2\(\vec{A} + \vec{B}\)| =** [ ] \(\text{m}\)
- Click **Submit**
### Explanation of Visuals
There are no graphs or diagrams in this problem, only text and input forms. The input forms are for submitting numerical answers for the angle in degrees and the magnitude of the resulting vector. The segments are clearly delineated with labels "Part A" and "Part B". There are buttons labeled "Submit" to confirm answers, and another option labeled "Request Answer" for assistance.
#### Note:
When solving these types of vector problems, recall that vectors are added component-wise. After performing the required operations, use trigonometric functions to find the direction and the Pythagorean theorem to find the magnitude.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd955a64d-1d84-4c4c-a975-e65e2fa2eacb%2F68524ae8-8a16-4b28-bf66-b657192b171a%2Fmnsf18j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Addition Problem
#### Given Vectors
- \(\vec{A} = (13.1 \, \text{m}) \hat{i}\)
- \(\vec{B} = (-31.7 \, \text{m}) \hat{j}\)
### Part A
**Problem:** Find the direction of the vector \(2\vec{A} + \vec{B}\).
**Solution Step:**
1. Calculate \(\theta\)
2. Input the result in the given form below.
#### Input Form:
- **θ =** [ ] \(^\circ\) below the \(+x\)-axis
- Click **Submit**
### Part B
**Problem:** Find the magnitude of the vector \(2\vec{A} + \vec{B}\).
**Solution Step:**
1. Calculate the magnitude.
2. Input the result in the given form below.
#### Input Form:
- **|2\(\vec{A} + \vec{B}\)| =** [ ] \(\text{m}\)
- Click **Submit**
### Explanation of Visuals
There are no graphs or diagrams in this problem, only text and input forms. The input forms are for submitting numerical answers for the angle in degrees and the magnitude of the resulting vector. The segments are clearly delineated with labels "Part A" and "Part B". There are buttons labeled "Submit" to confirm answers, and another option labeled "Request Answer" for assistance.
#### Note:
When solving these types of vector problems, recall that vectors are added component-wise. After performing the required operations, use trigonometric functions to find the direction and the Pythagorean theorem to find the magnitude.
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