Projectile motion analysis in the presence of dissipative forces for the high speed regime

In this work, we developed the equations regarding the movement of a smooth sphere in the presence of drag forces, in the high-speed regime, where the resistive force is proportional to the square of its velocity. This regime is commonly found in various everyday situations in which objects of all kinds are thrown into the air. The equations studied in basic undergraduate courses disregard the drag of the air and, therefore, are idealized equations, not consistent with the actual nature of the observed movement. Here, we intend to assist the reader in traveling a bit closer to reality and contemplating the complexity of some equations when we try to model the world as it truly is. This subject is of extreme importance for undergraduate students in the field of aeronautical engineering and mechanics, as it is essential to understand how drag forces affect the behavior of objects in motion.

Keywords
Projectile motion; Equations of motion; Drag force