Approximated Solutions of Optimal Angle in Extended Projection Model of a Point Mass

Abstract

Abstract. We investigate the optimal angle at which the flight range of a point mass is maximized on the basis of the extended projection model in which the initial speed decreases monotonously with the increase of the projection angle. The cubic equation of the projection angle is derived from the maximization problem of the flight range. Perturbed and asymptotic solutions of the equation are presented by using the singular perturbation method in order to clarify the features of the exact solution. The accuracy of these approximated solutions is evaluated and the dependency of model parameters to the solutions is clarified.