A rocket is set for vertical firing If the exhaust speed is `1200ms^(-1)` , how much gas must be ejected per second to supply the thrust needed (i) to overcome the weight of rocket (ii) to give to the rocket an initial vertical upward acceleration of `29.6 m//s^(2)` Given mass of rocket = 6000 kg.

Explanation

To solve the problem, we need to calculate the amount of gas that must be ejected per second to provide the necessary thrust for two scenarios: (i) to overcome the weight of the rocket, and (ii) to give the rocket an initial vertical upward acceleration of \(29.6 \, \text{m/s}^2\).

### Given Data:
- Exhaust speed, \(v = 1200 \, \text{m/s}\)
- Mass of the rocket, \(m = 6000 \, \text{kg}\)
- Acceleration due to gravity, \(g = 10 \, \text{m/s}^2\) (approximate value)

### Step 1: Calculate the weight of the rocket
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