Approximate analytical investigation of projectile motion in a medium with quadratic drag force

International Journal of Sports Science and Engineering. Vol. 05 (2011) No. 01, pp. 027-042The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account in the form of a quadratic function of velocity with the coefficient of resistance assumed to be constant. Analytical methods for the investigation are mainly used. With the help of simple approximate analytical formulas a full investigation of the problem was carried out. This study includes the determining of eight basic parameters of projectile motion (flight range, time of flight, maximum ascent height and others). The study also includes the construction of the basic functional dependences of the motion, the determination of the optimum angle of throwing, providing the greatest range; constructing of the envelope of a family of trajectories of the projectile and finding the vertical asymptote of projectile motion. The motion of a baseball is presented as examples.