Various methods for solving the pursuit problem with two objects on a plane

Abstract

Abstract We shall consider the classical problem of pursuit which can be described as follows. If object A (the pursued) moves along a known trajectory, then object B (the pursuer) which has a higher speed describes a pursuit trajectory (the chase trajectory) if B is always directed towards A. This article examines only the simplest two-dimensional case where the pursued moves rectilinearly, both the pursuer and the pursued have constant velocities, and the speed of the pursuer is γ times greater than that of the pursued. The different methods for solving the pursuit problem on a plane presented in this article require various levels of knowledge in mathematics as well as basic principles of two-dimensional kinematics. By learning pursuit problem, undergraduate students will be trained to solve the more complicated problems associated with this. On the other hand, the pursuit problem is convenient for Problem Based Learning as well as opportunity for animation of pursuit curves.