4500 J of energy is used to raise an object with a mass of 50 kg to a height h. Calculate h.

Answer

To solve the problem of calculating the height \( h \) to which an object is raised using 4500 J of energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Potential Energy**:
The potential energy (PE) gained by an object when it is raised to a height \( h \) is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the object (in kg),
- \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

2. **Identify the Given Values**:
From the problem, we have:
- \( PE = 4500 \, \text{J} \)
- \( m = 50 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)

3. **Set Up the Equation**:
Substitute the known values into the potential energy formula:
\[ 4500 = 50 \times 10 \times h \]

4. **Simplify the Equation**:
Calculate \( 50 \times 10 \):
\[ 50 \times 10 = 500 \]
So, the equation simplifies to:
\[ 4500 = 500h \]

5. **Solve for \( h \)**:
To find \( h \), divide both sides of the equation by 500:
\[ h = \frac{4500}{500} \]

6. **Calculate the Value of \( h \)**:
Performing the division:
\[ h = 9 \, \text{m} \]

### Final Answer:
The height \( h \) to which the object is raised is \( 9 \, \text{meters} \).

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