Here is my entry, it has a range of 15-19 feet.
The bottom is water bottle box, and the supporting posts are made from toilet paper tubes, stapled to the box and each other. The pivot is a wire coat hanger made from especially heavy wire (linemen’s pliers only made a small nick!

) and the arm is a cardboard tube that was originally on the hanger. I used a punching balloon to provide tension; to fire it you just pull down on the box end of the arm and let go when you are ready. The box to hold the ping-pong ball is an origami box made from an index card by my little brother, who also helped with the construction. The balloon, hanger, and guide tube (the one in the center of the box) are held in place with pipe cleaners, and the support tubes are wrapped with index cards for greater strength.
Materials used: Toilet paper tubes, cardboard box for the base, pipe-cleaners, staples, coat hanger, balloon, index cards.
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"It's like timing a monkey!"-me (explanation avalible by PM request)
"You can't spread Democracy with the barrel of a gun" ~ Helen Thomas
2006 Great Lakes Regional Semi-Finalists (Thanks to our allies: Team 66 and Team 68)
Thanks 469 for lending us your old OI in ATL!