A stone of mass 1 kg falls to the earth from a height of 10 m. The kinetic energy of the stone when it is 4 m above the ground is:

Options

A. 58.8 J
B. 5.88 J
C. 588J
D. none of these

Answer

To find the kinetic energy of the stone when it is 4 m above the ground, we can use the principle of conservation of mechanical energy. The total mechanical energy (potential energy + kinetic energy) at the initial height will be equal to the total mechanical energy at the height of 4 m.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the stone (m) = 1 kg
- Initial height (H) = 10 m
- Height above the ground when we want to find kinetic energy (h') = 4 m
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)

2. **Calculate the Initial Potential Energy (PE_initial):**
- The potential energy at the initial height (10 m) can be calculated using the formula:
\[ PE_{\text{initial}} = m \cdot g \cdot H \]
- Substituting the values:
\[ PE_{\text{initial}} = 1 \cdot 9.8 \cdot 10 = 98 \text{ Joules} \]

3. **Calculate the Potential Energy at 4 m Height (PE_final):**
- The potential energy at the height of 4 m can be calculated using:
\[ PE_{\text{final}} = m \cdot g \cdot h' \]
- Substituting the values:
\[ PE_{\text{final}} = 1 \cdot 9.8 \cdot 4 = 39.2 \text{ Joules} \]

4. **Use Conservation of Energy to Find Kinetic Energy (KE_final):**
- According to the conservation of mechanical energy:
\[ PE_{\text{initial}} = PE_{\text{final}} + KE_{\text{final}} \]
- Rearranging the equation to find the kinetic energy:
\[ KE_{\text{final}} = PE_{\text{initial}} - PE_{\text{final}} \]
- Substituting the values:
\[ KE_{\text{final}} = 98 - 39.2 = 58.8 \text{ Joules} \]

5. **Final Answer:**
- The kinetic energy of the stone when it is 4 m above the ground is **58.8 Joules**.