You can do similar to what paintball guns do. Most paintball guns either operate on a spool or poppet valve. I posted a link below of an animation of a spool valve. Essentially there is a bolt that is actuated by air. The bolt in a cylinder is similar to a piston but instead the bolt is a hollow tube that has hole through it and a flange at the back to seal the cylinder. At the back of the cylinder is a pin with an oring on it that rides in and out of the hole of the bolt. When compressed air is introduced into the rear, the bolt moves forward til the oring completely exits the bolt, letting air pass through the bolt. The function of this is two fold. The bolt moves forward initially for a short distance to accelerate the ball. This initial acceleration is key because if the ball was to be propelled only by air from the rest, the pressure in the compressed air would have to be incredibly high to propel the ball. Once the initial acceleration is generated, the air accelerates the ball further once the bolt clears the rear oring. Since the initial acceleration is generated by the bolt, very little air is necessary to propel it further. This is why most new paintball guns operated at pressures between 65-120psi depending on how fast you want the ball to travel. An increase in pressure, increases speed and vice versa. This could be theoretically done for a competition like this if FIRST ever allowed to have multiple compressors or a single large capacity compressor, with a large storage tank or multiple small ones to generate enough volume. The pressure restrictions would not have to be changed all that much. Also most paintball guns employ the same solenoids we use to toggle between shooting and reloading.
http://www.zdspb.com/media/tech/anim...p_g4_stock.gif