From the BBC’s Bang Goes the Theory site.

Full instructions can be found here.

Rockets work by ejecting something out of the back and a so-called ‘reaction force’ then pushes the body of the rocket forward.

Here, water and air are shoved out the back. The water is heavier so that’s what gives the bottle the main kick forwards.

The energy to force the water out is stored as air pressure inside the bottle. You supply the energy as you pump air into the bottle.

The air pressure inside builds up and pushes on the water. But friction holds the cork in place and that pushes back on the water, so for a while nothing moves.

Once the friction force can no longer contain the pressure, the cork is shoved out and the pressure then acts on the water to eject it from the bottle.

Compared to the bottle, the water is heavy. So pushing water out at a moderate speed backwards gives the bottle a lot of forward speed.