Consider a free particle in a plane. Using Cartesian coordinates, it is trivial to show that the

Question:

Consider a free particle in a plane. Using Cartesian coordinates, it is trivial to show that the particle moves in a straight line. The task of this problem is to demonstrate this result in a much more cumbersome way, using eqs. (2.52). More precisely, show that cos ? = r0/r for a free particle, where r0 is the radius at closest approach to the origin, and ? is measured with respect to this radius.