Catapults use levers, counterweights and the principles of projectile motion to launch their payloads. The throwing arm of the catapult acts as a lever and has a bucket on the end that contains the desired projectile. The counterweight, when released, allows the catapult to launch.
Some models of catapults include crossbars that stop the arm from moving past a certain angle. By controlling the distance the arm can move, it influences when the projectile is released and therefore the launch angle. A higher launch angle provides more height but less horizontal distance.
A catapult relies on torque, which is a function of the length of the arm and the speed at which it moves, to provide angular momentum to the projectile..After the payload leaves the catapult, the only forces acting on it are gravity and wind resistance. Therefore, when calculating motion, the standard kinematic equations apply. For example, determining the range requires knowledge of the horizontal velocity and launch angle, as well as flight time.
The formula for horizontal velocity is vx = cos(theta)Vo, or the cosine of the launch angle multiplied by the original velocity. Then, the time of flight is required. The time of flight cab be found with the formula 2vy/g, where g is 9.8 and vy is the vertical velocity, or the original velocity multiplied by the sine of the launch angle. Finally, multiplying the horizontal velocity by the time of flight yields the range.