The "bottle rocket" is able to "fly" because of the use of water and pressure, created with a chemical reaction between the mentos and baking soda. Whereas other kinds of compression can be used, such as cylinders of CO2, compressed air or nitrogen, the air in the bottle is pressurized by the gases released when combining (most likely) the sugar from the mints and baking soda. (You may recall simulating a volcanic reaction by adding vinegar to baking soda: this chemical reaction releases energy.) When the reaction takes place, the pressure must go somewhere. With no other outlet, the gases force the water from the bottle, and the release of this water propels the "rocket" into the air as the water escapes at a violent speed.
This experiment is directly related to illustrating "aeronautics."
The following concepts are connected to the bottle rocket...
...inertia, gravity, air resistance, Newton's laws of motion, acceleration, relationships between work and energy or impulse and momentum, projectile motion, etc.
The water bottle is the water rocket's "engine." The fuel (in your case) is the mints and the baking soda—which cause combustion: the burst of energy needed to raise the rocket. The loss of water from the bottle lightens the weight and allows for the rocket to climb higher.
Build up of the carbon dioxide from the mentos and baking soda causing the pressure to be so immense something has to release it.