A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rocket’s speed 10 s, 20 s, and 30 s after launch?

Explanation:

The speed of the rocket is given the Tsiolkovsky's differential equation, whose solution is:

Where:

- Initial speed of the rocket, in m/s.

- Exhaust gas speed, in m/s.

- Initial total mass of the rocket, in kg.

- Current total mass of the rocket, in kg.

Let assume that fuel is burned linearly. So that,

The initial total mass of the rocket is:

The fuel consumption rate is:

The function for the current total mass of the rocket is:

The speed function of the rocket is:

The speed of the rocket at given instants are:

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