A space shuttle while travelling at a speed of 4000 km/h with respect to the earth disconnects and ejects a module backward, weighing one sixth of the residual part. If the shuttle ejects the disconnected module at a speed of 100 km/h with respect to the state of the shuttle before the ejection, find the final velocity of the shuttle.

Explanation

To solve the problem, we will use the principle of conservation of momentum. Here’s the step-by-step solution:

### Step 1: Define the Variables
Let:
- \( V_s = 4000 \) km/h (initial speed of the shuttle with respect to Earth)
- \( V_m = 100 \) km/h (speed of the module with respect to the shuttle)
- \( M \) = initial mass of the shuttle
- \( m = \frac{M}{6} \) = mass of the ejected module
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