mgh = 1 mv ₁ ² 2 Duph FAST 2 m = 1.00 kg 9 = 9.80 m/s² V₁ = 11 m/s 2 Solve for hieght (h)

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Chapter1: Units, Trigonometry. And Vectors
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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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### 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:
   \[ h = \frac{v_i^2}{2g} \]
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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