I need to make a cannon that fires a marble. It must be accurate and adjustable enough to hit targets of varying distance and through varying obstacles. For propellant, I want to use compressed air, for which I have an apparatus (valve from a bike tire attached to a PVC cylinder roughly fifteen centimetres long. The cylinder is about five centimetres wide. A quick release valve attached to a string will be the trigger mechanism. The question is, how much pressure should I load the tank up with to shoot a 5.4 g marble at around 5 metres per second? My first thought was to use energy: E = Volume(V) x Pressure(P), but I am not sure this is the correct way to do this, mainly because I haven't actually learned this equation in physics class, but I came up with it based on unit analysis during chemistry class. I am not sure what assumptions are made by the equation for example. My best attempt: Atmospheric pressure in my classroom is about 14.7 PSI (we measured this in our chemistry class just across the hall) and all of the compressed air will be discharged after every shot. Or rather, enough air will leave the cylinder such that the pressure inside the tank is equal to the pressure outside the tank. If the seal is totally air tight and the pressure perfectly equalizes, the Kinetic energy of the marble after leaving the barrel should be equal to the volume of the cylinder times the difference in pressure (initial pressure in tank minus atmospheric pressure). Is this correct? Again note that I haven't actually learned this formally.