A rocket moves forward by pushing the surrounding air backwards.

Step 1: Analyze the given statement.

The statement asserts that a rocket moves forward by pushing the surrounding air backwards.

Step 2: Examine the propulsion mechanism.

The rocket engine expels its own exhaust gas backward at speed $u$, which is carried aboard as propellant rather than taken from the surrounding air.

Step 3: Apply Newton's Third Law.

The action of expelling gas backward produces an equal and opposite reaction force that pushes the rocket forward.

$$\vec{F}_{\text{rocket} \to \text{gas}} = -\vec{F}_{\text{gas} \to \text{rocket}}$$

Step 4: Apply conservation of momentum.

The total momentum of the rocket and the exhaust gas remains conserved.

$$\vec{p}_{\text{gas}} + \vec{p}_{\text{rocket}} = 0$$ $$M V = m_{\text{gas}} u$$

Step 5: Express the thrust force.

The thrust force $F$ is determined by the mass flow rate and the exhaust velocity.

$$F = \frac{dm}{dt} u$$

This formula contains no term for the surrounding air, showing that thrust is independent of the atmosphere.

Step 6: Calculate acceleration for a sample case.

For a mass flow rate of $2\text{ kg/s}$, exhaust speed of $2000\text{ m/s}$, and rocket mass of $1000\text{ kg}$, we find the thrust and acceleration.

$$F = 2 \times 2000 = 4000\text{ N}$$ $$a = \frac{F}{M} = \frac{4000}{1000} = 4\text{ m/s}^2$$

Step 7: Evaluate the requirement of air.

Since the propellant is carried entirely on board, the rocket does not require surrounding air and can operate in a vacuum.

Answer: The statement is False. A rocket moves forward by expelling its own propellant backward (in accordance with Newton's third law), and its propulsion is entirely independent of the surrounding air.