Question

A rocket takes off from Earth and reaches a speed of 100 m/s in 10.0 s. If the exhaust speed is 1500 m/s and the mass of fuel burned is 100 kg, what was the initial mass of the rocket?

a) 2000 kg
b) 2200 kg
c) 2400 kg
d) 2600 kg

Answer 1

The initial mass of the rocket was 2400 kg.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum. The change in momentum of the rocket is equal to the momentum imparted to the exhaust gases. The initial momentum of the rocket is zero because it starts from rest, and the final momentum is the mass of the rocket multiplied by its final velocity. The change in momentum of the gases is the mass of the fuel burned multiplied by the exhaust speed. Equating these two expressions and solving for the initial mass of the rocket:

Initial momentum of rocket = Final momentum of rocket

0 = (mass of rocket + mass of fuel burned) × final velocity of rocket - mass of fuel burned × exhaust speed

Simplifying this equation:

Initial mass of rocket = mass of fuel burned × (exhaust speed - final velocity of rocket) / final velocity of rocket

Substituting the given values:

Initial mass of rocket = 100 kg × (1500 m/s - 100 m/s) / 100 m/s = 2400 kg

Therefore, the initial mass of the rocket was 2400 kg.