When an object is catapulted, it is subject to both the force of gravity and the force from the catapult. The catapult applies a force to the object in both the horizontal (forward) and vertical (upward) directions, and gravity pulls the object vertically downward. The horizontal component of the catapult force makes the object go forward in the direction the catapult throws the object, and the vertical component of the catapult force allows the object o go up. At the same time, the downward force of gravity means that the object will only go up a certain distance before it starts to come down again.

Combining the two vertical forces and one horizontal force, we will then see the object make an arc in the air and eventually land. Depending on how heavy the object is and how much surface area it has, air resistance may also affect the object. If the object has a large surface area, air resistance will act against the horizontal force of the catapult and slow down the object, making the object not travel as far as another object that has less surface area.

Objects thrown by a catapult are subject to all of the laws of Physics! The throwing of the object is subject to the law of conservation of energy (i.e. the potential energy stored in tension gets transferred to the object you're flinging) as well as the laws of gravity that pull it down at all times. The object will experience a significant amount of friction in the air too as it pushes away the air molecules in its way. Basically, all of the laws still apply.

My old neighbor built a catapult in his driveway - or maybe it was a trebuchet. Trebuchets are a type of catapult. MythBusters have an episode of their show where they build a big trebuchet that is only held together by duct tape. Here's the preview: trebuchet.

Here's a website about catapult physics: catapult physics.

Everything is determined by the laws of physics. The force that the catapult exerts on the object is determined by physics. The arc that the thrown object takes while moving through the air is determined by the laws of physics. The effect of the impact when the object hits the ground is determined by physics.