Pop Bottle Cannon Math?

Alot of energy will be lost due to the lateral and downward forces resulting from your blast. Unless its a perfect or near perfect vacuum the resulting resistance will dampen your enertia. Imagine shooting a real cannon. Instead of using gun powder packed into the rear, you put a hand grenade in for your charge. All the force from the blast are not aligned in the same direction. Your idea sounds interesting but there's no math formula to answer your questions.