If the subject is conservation of energy, then you are likely supposed to approach the problem by taking the gas and the rocket as an isolated system. Notice that when both are stopped mechanical energy is zero.
By the law of conservation, the energy is the same in an isolated system if no external forces are applied. Since all forces involved are interactions between of the rocket and the gas, all forces are internal and energy must conserve.
So, what is the kinetic energy of the gas after it is propelled out? What is the relation of this energy with the kinetic energy of the rocket? Tip: you can convention energy to be negative in a specific situation.