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)...
Related questions
Question
![### Problem Statement
"From the top figure, what is the final velocity of the 5 kg ball?"
### Diagrams and Equations
The board presents a scenario involving two balls and related equations:
1. **Context:**
- A 5 kg ball moving at 12 m/s collides with a 3 kg ball moving at 4 m/s.
- The angles given for the post-collision velocities:
- 5 kg ball moves at \(30^\circ\).
- 3 kg ball moves at \(45^\circ\).
2. **Equations:**
- \(\cos^2 \theta + \sin^2 \theta = 1\) - Basic trigonometric identity.
- Given relation:
\[
44 = 8V^2(\cos^2 \theta + \sin^2 \theta)
\]
- Simplified to find velocity \(V\):
\[
V = \sqrt{\frac{44}{8}}
\]
### Multiple Choice Options
- 11.9
- 10.1
- 6.7
- 8.4
- 14.6
### Diagram Explanation
The diagrams indicate initial velocities and directions of the balls before and after the collision, along with the necessary vector components to apply conservation laws.
### Solution Approach
Using the conservation of momentum and kinetic energy principles, one can derive the final velocity \(V\) of the 5 kg ball using the provided equations and check against the given answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc1a7a38-25d3-462e-b7c4-fed79074d810%2F07fe56c4-cc33-49c5-924a-1ae6df9ec638%2F42ao9fp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
"From the top figure, what is the final velocity of the 5 kg ball?"
### Diagrams and Equations
The board presents a scenario involving two balls and related equations:
1. **Context:**
- A 5 kg ball moving at 12 m/s collides with a 3 kg ball moving at 4 m/s.
- The angles given for the post-collision velocities:
- 5 kg ball moves at \(30^\circ\).
- 3 kg ball moves at \(45^\circ\).
2. **Equations:**
- \(\cos^2 \theta + \sin^2 \theta = 1\) - Basic trigonometric identity.
- Given relation:
\[
44 = 8V^2(\cos^2 \theta + \sin^2 \theta)
\]
- Simplified to find velocity \(V\):
\[
V = \sqrt{\frac{44}{8}}
\]
### Multiple Choice Options
- 11.9
- 10.1
- 6.7
- 8.4
- 14.6
### Diagram Explanation
The diagrams indicate initial velocities and directions of the balls before and after the collision, along with the necessary vector components to apply conservation laws.
### Solution Approach
Using the conservation of momentum and kinetic energy principles, one can derive the final velocity \(V\) of the 5 kg ball using the provided equations and check against the given answers.
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