The conversation between human and AI assistant.
In water rockets, I found this equation: h= (Mi/Mr) * (Mi/Mr) * (Pi/density of water*g). How did I get this equation?
I see. So how does that relate to the equation I found?
The rocket altitude equation is obtained by solving the energy conservation principle with respect to the height reached by the rocket. The initial energy of the system can be expressed in terms of the initial mass Mi, the gravitational constant g, and the initial height hi, which is usually set to zero. The final mass Mr is the mass of the rocket plus the mass of the expelled water, which is given by the product of the density of water and the volume of water expelled, which is proportional to the initial mass. Finally, the final internal energy of the system can be expressed in terms of the pressure of the gas used to propel the rocket, which is usually air, and the volume of the rocket. By substituting these expressions into the energy conservation equation and solving for the height, we obtain the rocket altitude equation that you found.