A Rocket having initial mass `5xx10^(6)kg` , which include mass of fuel of mass `4xx10^(6)kg` is ejecting gas with velocity `4000m//s` relative to Rocket. Then what will be the velocity of rocket when entire fuel finishes?

Explanation

To solve the problem, we will use the rocket equation derived from the conservation of momentum. The equation relates the change in velocity of the rocket to the mass of the rocket and the velocity of the ejected gas.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Initial mass of the rocket, \( m_i = 5 \times 10^6 \, \text{kg} \)
- Mass of the fuel, \( m_f = 4 \times 10^6 \, \text{kg} \)
- Velocity of the ejected gas, \( v_g = 4000 \, \text{m/s} \)
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