With what velocity must a body be thrown from earth's surface so that it may reach a maximum height of `4R_(e)` above the Earth's surface ? (Radius of the Earth `R_(e)=6400 km,g=9.8 ms^(-2)`).

Explanation

To find the velocity with which a body must be thrown from the Earth's surface to reach a maximum height of \(4R_e\) above the Earth's surface, we can use the principle of conservation of mechanical energy.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the Earth, \(R_e = 6400 \, \text{km} = 6400 \times 10^3 \, \text{m}\)
- Acceleration due to gravity, \(g = 9.8 \, \text{m/s}^2\)
- Maximum height above the Earth's surface, \(h = 4R_e = 4 \times 6400 \times 10^3 \, \text{m}\)
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