Projectile motion in a resistant medium Part 1: exact solution and properties

The motion of a particle which is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle speed squared. The problem is formulated in terms of particle-speed and local-path-angle variables, and the equations of motion that result are non-linear and coupled. A new technique is presented which provides an exact time-implicit solution to these equations in the form of a parametric description of the particle motion. This description is utilized to obtain exact conditions from which the maximum projectile range and the optimal projection angle can be determined to any desired degree of precision. This description also reveals general properties of the projectile trajectory, some of which motivate the development of an approximate solution. (C) 2002 Elsevier Science Ltd. All rights reserved.