The launching of a waterjet rocket has been a very popular idea in recent years. Its basic propulsion principle makes use of the high-pressurized air inside the rocket's main body to swiftly expel the water out of the nozzle and thus generate thrust. The waterjet rocket is characterized with nature, interest, combustionlessness, environmental friendliness, simplicity, and minimal cost. Moreover, it is a very good science model for propulsion analysis, design, experiment, and education because of an abundance of easily adjustable key parameters. This model also features separately stored energy and mass of the propellant, in contrast to a conventional rocket. However, related literature shows that no indepth theoretical analysis of the waterjet rocket has been attempted for various reasons. In this research, the propulsion dynamics of a waterjet rocket is analyzed by simultaneously solving the momentum and the newly derived generalized power equations to predict its flight histogram, computationally, and convolutionally. This integrated energy approach synthesizes the internal and external dynamics analyses together and ingeniously takes full advantage of the clear power supply of pressurized air in a waterjet rocket. The analysis results are generally agreeable with the experimental flight data. While the new power equation herein gives a complete spectrum of physical parameters to be manipulated, there will be wider room in quest of better rocket propulsion performance, especially through the heuristic research of this versatile but affordable waterjet rocket.