Questions: Rocket Propulsion and Variable-Mass Systems

Question 1

A rocket in deep space starts at rest. Its exhaust speed relative to the rocket is 3000 m/s. It burns fuel until its mass falls from m₀ to m₀/e², where e ≈ 2.718. What is its final speed?

• A. 1500 m/s
• B. 3000 m/s
• C. 6000 m/s
• D. 22,000 m/s

Answer: (C)

Δv = v_e ln(m₀/m_f) = 3000 m/s × ln(e²) = 3000 × 2 = 6000 m/s.

Question 2

A rocket engine would produce no thrust in the vacuum of space, because there is no air for the exhaust to push against.

• T. True
• F. False

Answer: False

Thrust comes from the momentum given to the exhaust. By momentum conservation, the rocket gains equal and opposite momentum. No outside medium is needed.

Question 3

A rocket has mass ratio m₀/m_f = 4. Which change gives the larger final speed: doubling the exhaust speed, or doubling the mass ratio to 8?

• A. Doubling the exhaust speed
• B. Doubling the mass ratio
• C. Both give the same final speed
• D. Neither changes the final speed

Answer: (A)

Doubling v_e doubles Δv, from v_e ln 4 to 2v_e ln 4. Doubling the mass ratio gives v_e ln 8 = 1.5 v_e ln 4, only 50% more.

Question 4

An engine ejects 40 kg of gas per second at 2500 m/s relative to the rocket. What thrust does it produce?

Model answer: 100,000 N (100 kN)

Thrust = v_e |dm/dt| = 2500 m/s × 40 kg/s = 1.0 × 10⁵ N.