The Effect of Air Resistance on projectiles Motion equation and study General Solution with air resistance quadratic in the speed

Abstract

This research work study the a projectiles motion without air resistance and  projectiles motion with air resistance by using vector-valued function. We consider two-dimensional motion of a projectile experiencing a constant gravitational force  in the projectile’s speed and  look at launching projectiles, as well as how varying initial velocity and height affect the launch angle. Finally, we add air resistance to the projectile problem and compare two different models: air resistance proportional to the projectile’s velocity and air resistance proportional to velocity squared

 We find that :The equations of motions are coupled nonlinear equations. Their solutions have general properties which are easily visualized, although much different from those obtained when an air resistance  is  neglected.