The answer is that you gain velocity by shooting rocket fuel out the back. The energy that the fuel loses is proportional to the the square of the speed of the

The answer is that you gain velocity by shooting rocket fuel out the back. The energy that the fuel loses is proportional to the the square of the speed of the rocket as well, so everything works out fine. The mass of the rocket fuel is small, but it's not negligible, especially considering that kinetic energy is far more concerned with velocity than with mass.