### Problem Statement"From the top figure, what is the final velocity of the 5 kg ball?"### Diagrams and EquationsThe 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 ExplanationThe 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 ApproachUsing 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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Answered: From the top figure, what is the final…

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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

### 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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