E.Browne,
Whether the projectile issues from a catapult, a slingshot, a rifle, a star, or a flashlight the basic mechanical problem is the same. The problem being that to use anyone of those things you have to know where the projectile will be at some time in the future and how much energy it will have when it gets there.
After the projectile leaves the instrument you have no control over it at all. Then comes the "art-science" of ballistics.
The ballistics information on a box of rifle ammunition gives you that information, for that particular cartridge, often laid out very nicely.
I thought that seeing a chart laid out like that would give a student some ideas on making a chart of his own with the particulars of his particular machine in mind.
Since catapults are mostly used in similar environments to a rifle the major differences will be in the increase of air resistance at higher speeds.
Since we as of yet have no knowledge of where he wishes to use this machine discussing trajectories in different environments would be a bit premature.
A further instance. The rifling changes the response of a projectile to air pressure by allowing a smaller frontal area for a given amount of mass, and maintaining that attitude.
On the moon a "slug" would do as well!
Thats a good link