Question

A rocket at rest on the ground with initial mass 20,000 kg, 80% of which is fuel, burns 200kg/s as it flies

directly upwards. The exhaust gas exits the rocket at a relative speed of 1.80 km/s. Find (a) the thrust of

the rocket, (b) how long it takes to exhaust its fuel, and (c) the rocket’s speed at the end of its engine burn.

Assume g is constant and neglect air resistance.


For Part A I got: 360,000 Newtons, Part B: 20 Seconds, Part C 205.658 m/s

Are my answers correct?

Answer 1

To check your answers, we can use the following equations:

(a) Thrust = (mass flow rate of exhaust gas) * (exhaust velocity of gas) + (initial mass of rocket) * (acceleration due to gravity)

(b) Time to exhaust fuel = (0.8 * initial mass of rocket) / (mass flow rate of exhaust gas)

(c) Final velocity of rocket = (exhaust velocity of gas) * ln(initial mass of rocket / final mass of rocket)

Using the given values:

Mass flow rate of exhaust gas = 200 kg/s

Exhaust velocity of gas = 1.80 km/s = 1800 m/s

Initial mass of rocket = 20,000 kg

Acceleration due to gravity = 9.81 m/s^2

Final mass of rocket = 0.2 * initial mass of rocket = 4,000 kg

(a) Thrust = (200 kg/s) * (1800 m/s) + (20,000 kg) * (9.81 m/s^2) = 360,000 N

Your answer for part (a) is correct.

(b) Time to exhaust fuel = (0.8 * 20,000 kg) / (200 kg/s) = 800 s = 20 minutes

Your answer for part (b) is incorrect. The correct answer is 800 seconds or 20 minutes, not 20 seconds.

(c) Final velocity of rocket = (1800 m/s) * ln(20,000 kg / 4,000 kg) = 205.66 m/s

Your answer for part (c) is correct.