In loving memory of THE WIDOW MAKER, I thought I would bring back some old-school physics.
Well, our catapult launches the ball at a certain velocity (v), directed at, let's say, 45 degrees upward. For projectiles, you have to break the velocity into an upward and a horizontal velocity. The upward velocity is v sin(45) and the horizontal velocity is v cos(45), so they are both .707v. The reason you do this is because the projectile travels to its highest point with its upward velocity in the same amount of time it travels half of its range with its horizontal velocity. You can find this time (t) using the formula v=vi+at: 0=.707v - 9.8(t), so t =.072v.
In this time, the object travels half of its range, so in twice this time the object travels its full range (lat's call it 50 meters). d = v*t, so 50 = .707v(2)(.072v), 50 = .1018 v^2, so v = 22.2 meters/second.
However, we aren't in a perfect world, and THE WIDOW MAKER is not the perfect catapult (supposedly), so unfortunately it did not travel 50 meters, it traveled about half of that. Also, it snapped in half too...
Sincerely, and in loving memory of THE WIDOW MAKER,