Investigation Of Projectile Motion with Altitude Dependent Quadratic Drag Force

Abstract

The problem of projectile motion without frictional force is an age-old problem as it is exactly solvable. The problem has also been revisited in a resisting medium with quadratic damping.  The damping constant depends on the density of the medium. All the recent calculations solve the problem with a constant dragging force. However, if the projectile is launched from a height, it will traverse several layers of air of wide varying density specially during the downward motion. As the dragging force is quadratic with the velocity, the altitude dependent dragging force will have immense effect on the trajectory if it is projected with high velocity.  We apply a simple python code to study the trajectory of the projectile in a very realistic situation as varying dragging force is taken into account. We present an exhaustive study with varying launching height and launching angle. We also obtain a graphical nature of dependence of optimized angle to obtain the maximum range.