At a point above the surface of the earth, the gravitational potential is `-5.12 xx 10^(7)` J/kg and the acceleration due to gravity is `6.4 m//s^(2)`. Assuming the mean radius of the earth to be 6400 km, calculate the height of the point above the earth's surface.

Explanation

To solve the problem, we will use the formulas related to gravitational potential and acceleration due to gravity.

### Step-by-Step Solution:

1. **Understand the Given Values:**
- Gravitational potential \( V = -5.12 \times 10^7 \, \text{J/kg} \)
- Acceleration due to gravity \( g = 6.4 \, \text{m/s}^2 \)
- Mean radius of the Earth \( R = 6400 \, \text{km} = 6400 \times 10^3 \, \text{m} = 6.4 \times 10^6 \, \text{m} \)
...