A catapult is used to throw things. If, for example, you look at the trebuchet, you see that it has a very heavy load, heavier then the projectile, that is set up above the ground. This gives the load and consequentially the trebuchet a lot of potential energy. The projectile is launched when the load starts to fall on the ground, when it's falling, it gets kinetic energy which is given to the projectile. The projectile uses it to build up potential energy as it flies towards it's goal, and then gains back the kinetic energy as it falls.
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