College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Physics Problem: Solving for Height Using Energy Conservation
**Given Equation:**
\[ mgh = \frac{1}{2} mv_i^2 \]
**Variables:**
- \( m = 1.00 \, \text{kg} \) (mass)
- \( g = 9.80 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( v_i = 11 \, \text{m/s} \) (initial velocity)
**Task:**
Solve for height (\( h \)).
### Explanation:
This problem involves using the principle of conservation of energy to determine the height to which an object will rise.
1. **Potential Energy** at a height \( h \) is given by \( mgh \).
2. **Kinetic Energy** at the initial velocity \( v_i \) is \( \frac{1}{2} mv_i^2 \).
Using the conservation of mechanical energy:
- The initial kinetic energy is converted into potential energy at height \( h \).
**Steps to Solve:**
1. Set \( mgh \) equal to the kinetic energy \( \frac{1}{2} mv_i^2 \).
2. Simplify the equation since \( m \) appears on both sides.
3. Solve for \( h \) by rearranging the equation:
\[ h = \frac{v_i^2}{2g} \]](https://content.bartleby.com/qna-images/question/70550eb8-aa65-4083-8eb4-f6c8d8ee1b0c/4657a7e4-6aea-4702-94ba-37056ea252a9/206bsmi_processed.jpeg)
Transcribed Image Text:### Physics Problem: Solving for Height Using Energy Conservation
**Given Equation:**
\[ mgh = \frac{1}{2} mv_i^2 \]
**Variables:**
- \( m = 1.00 \, \text{kg} \) (mass)
- \( g = 9.80 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( v_i = 11 \, \text{m/s} \) (initial velocity)
**Task:**
Solve for height (\( h \)).
### Explanation:
This problem involves using the principle of conservation of energy to determine the height to which an object will rise.
1. **Potential Energy** at a height \( h \) is given by \( mgh \).
2. **Kinetic Energy** at the initial velocity \( v_i \) is \( \frac{1}{2} mv_i^2 \).
Using the conservation of mechanical energy:
- The initial kinetic energy is converted into potential energy at height \( h \).
**Steps to Solve:**
1. Set \( mgh \) equal to the kinetic energy \( \frac{1}{2} mv_i^2 \).
2. Simplify the equation since \( m \) appears on both sides.
3. Solve for \( h \) by rearranging the equation:
\[ h = \frac{v_i^2}{2g} \]
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