Numerical Investigation of the Effect of Air Resistance on the Maximum Range of a Projectile

Abstract Projectile motion is an important concept in classical mechanics; butt the ideal model generally ignores the effect of air resistance. In real-world conditions,. Aerodynamic drag influences the t1r6ajectory, flight time, and horizontal range of a projectile. This study numerically investJgates maximum range a projectile. A mathematical model i7ncorporating quadratic air drag is developed to describe the projectile s horizontal and vertical solved numerically for different launch angles, initial velocities,. And drag conditions. The obtained trajectories and ranges are compared with those predicted by the ideal model without air resistance. Special attentfon is given to determining how air resistance changes the launch angle corresponding to maximum range. The study provides a computational approach for understanding realistic projectile motion and the limitations of the conventional idealized model.