Catapult math

[billbo911]

Sorry, I won't quote any equations except to say, 45 degrees is going to give maximum distance.

Now, maximum distance isn't always the optimal trajectory.

Putting a 24" dia. ball through a 37" opening requires fairly accurate positioning if you are throwing on a parabolic curve that is provided by a 45 deg. launch angle.

If you can't reach the bottom of the goal at 45 deg, then moving closer and increasing your launch angle will make it even harder to get the ball to pass through the goal, because the ball will be at the right height for a shorter distance.

A flatter trajectory might be a better choice as the ball will remain in the correct height range for a longer distance. Thus, you need to lower your launch angle. This also requires you to shoot a further distance.

Honestly, testing your shooter will help you figure out what exactly is your "optimal" angle.