To calculate the distance a catapult can launch a projectile, key factors include the spring constant, the stretch of the spring, the height of the launch point, and the mass of the projectile. The energy stored in the spring can be converted to kinetic energy, which requires knowing the initial velocity and launch angle. Accurate predictions depend on accounting for all forms of energy, including potential and rotational energy. Experimental calibration may simplify the process, but precise measurements yield better results. Overall, integrating the physics involved will enhance the accuracy of the launch distance prediction.