From the top figure, what is the final velocity of the 3 kg ball? 1にc050+ Sino (A)V LOSO 44-V(EosD+らん6) O 11.9 O 10.9 O 8.4 O 6.3 O 14.7

College Physics
11th Edition
ISBN:9781305952300
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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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### Problem Statement
From the top figure, what is the final velocity of the 3 kg ball?

### Whiteboard Explanation

The image displays a whiteboard with formulas, vectors, and diagrams involving physics and trigonometry. Below is a transcription and explanation of the content:

#### Equations and Calculations

1. **Fundamental Trigonometric Identity:**
   \[
   1 = \cos^2\theta + \sin^2\theta
   \]

2. **Equation for component resolution:**
   \[
   44^2 = 8v^2 \cos\theta
   \]

3. **Alternate equation:**
   \[
   0 = 8v^2 \sin\theta
   \]

4. **Solving for \(v\):**
   \[
   44^2 = 8v^2 (\cos\theta + \sin\theta)
   \]

   Rearranging gives:
   \[
   v = \text{(some expression)}
   \]

5. The calculations involve finding the velocity \(v\), using component resolution and combining trigonometric identities.

#### Diagrams

- **Vectors and Masses:**
  - A vector labeled \(V_1\) at 30° with a mass of 5 kg.
  - A vector labeled \(V_3\) at 45° with a mass of 9 kg.
  - Another vector with an unknown angle, labeled \(\Theta\).

#### Multiple-Choice Options

- 11.9
- 10.9
- 8.4
- 6.3
- 14.7

The question asks for the final velocity and presents options that may be derived from properly analyzing the provided mechanics problem and equations.

### Solution Notes

The correct solution can be arrived at by solving the equations listed, using trigonometric identities and understanding of vector resolution for dynamic systems in physics. This exercise involves skillfully applying knowledge of physics to solve for unknowns in a multi-step problem.
Transcribed Image Text:### Problem Statement From the top figure, what is the final velocity of the 3 kg ball? ### Whiteboard Explanation The image displays a whiteboard with formulas, vectors, and diagrams involving physics and trigonometry. Below is a transcription and explanation of the content: #### Equations and Calculations 1. **Fundamental Trigonometric Identity:** \[ 1 = \cos^2\theta + \sin^2\theta \] 2. **Equation for component resolution:** \[ 44^2 = 8v^2 \cos\theta \] 3. **Alternate equation:** \[ 0 = 8v^2 \sin\theta \] 4. **Solving for \(v\):** \[ 44^2 = 8v^2 (\cos\theta + \sin\theta) \] Rearranging gives: \[ v = \text{(some expression)} \] 5. The calculations involve finding the velocity \(v\), using component resolution and combining trigonometric identities. #### Diagrams - **Vectors and Masses:** - A vector labeled \(V_1\) at 30° with a mass of 5 kg. - A vector labeled \(V_3\) at 45° with a mass of 9 kg. - Another vector with an unknown angle, labeled \(\Theta\). #### Multiple-Choice Options - 11.9 - 10.9 - 8.4 - 6.3 - 14.7 The question asks for the final velocity and presents options that may be derived from properly analyzing the provided mechanics problem and equations. ### Solution Notes The correct solution can be arrived at by solving the equations listed, using trigonometric identities and understanding of vector resolution for dynamic systems in physics. This exercise involves skillfully applying knowledge of physics to solve for unknowns in a multi-step problem.
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