Projectile motion with air resistance

No input data. – 8 p.Suppose that a projectile of mass m is launched, at t=0, from ground level (in a flat plain), making an angle theta to the horizontal. Suppose, further, that, in addition to the force of gravity, the projectile is subject to an air resistance force which acts in the opposite direction to its instantaneous direction of motion, and whose magnitude is directly proportional to its instantaneous speed. This is not a particularly accurate model of the drag force due to air resistance (the magnitude of the drag force is typically proportion to the square of the speed), but it does lead to tractable equations of motion. Hence, by using this model we can, at least, get some idea of how air resistance modifies projectile trajectories.