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what my group did to eliminate the sling timing issue was we just taped a piece of string to the actual projectile and attached that to a pin that releases when the projectile and string reached the optimal spot in it's rotation to fly off on a 45 degree tangent. It took a little testing to get the angle of the pin perfect, but we didnt have to worry about the sling fucking up because there wasn't one.
sounds stupid and admittedly it's pretty lazy but our trebuchet shot flawlessly every time and threw things further than anyone else's. so we got 100% on it lol grade 12 physics was kind of a joke though