**Solution:**

To determine the amount of gas that must be ejected to give the rocket an upward acceleration of 20 m/s^2, we can use Newton's second law of motion. According to this law, the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force is the force generated by the ejected gas, and the mass is the mass of the rocket.

**Step 1: Calculate the force required**

The force required to give the rocket an upward acceleration of 20 m/s^2 can be calculated using the formula:

Force = mass × acceleration

Given:
Mass of the rocket (m) = 6000 kg
Acceleration (a) = 20 m/s^2

Substituting the values into the formula, we get:

Force = 6000 kg × 20 m/s^2
Force = 120,000 N

So, the force required to accelerate the rocket is 120,000 Newtons.

**Step 2: Calculate the mass of the ejected gas**

To find the mass of the ejected gas, we need to use the concept of conservation of momentum. According to this principle, the total momentum before and after the ejection of the gas should be equal.

The momentum before ejection is given by:

Momentum = mass × velocity

Given:
Velocity (v) = 1000 m/s (1 km/s)

Substituting the values into the formula, we get:

Momentum = (mass of rocket + mass of gas) × velocity

The momentum after ejection is given by:

Momentum = mass of rocket × final velocity

Since the final velocity is zero after the gas is ejected, the momentum after ejection is zero.

Therefore, we can set the two momentum equations equal to each other:

(mass of rocket + mass of gas) × velocity = mass of rocket × 0

mass of rocket + mass of gas = 0

mass of gas = -mass of rocket

**Step 3: Calculate the mass of the ejected gas**

Substituting the known values, we get:

mass of gas = -6000 kg

Therefore, the mass of the gas that must be ejected to give the rocket an upward acceleration of 20 m/s^2 is 6000 kg.

In summary, to give the rocket an upward acceleration of 20 m/s^2, 6000 kg of gas must be ejected.