  As we typically teach in an introductory mechanics course, choosing a "good"
reference frame with convenient axes may present a major simplification to a
problem. Additionally, knowing some conserved quantities provides an extremely
powerful problem-solving tool. While the former idea is typically discussed in
the context of Newton's Laws, the latter starts with introducing conservation
of energy even later.
  This work presents an elegant example of implementing both aforementioned
ideas in the kinematical context, thus providing a "warm-up" introduction to
the standard tools used later on in dynamics. Both the choice of the
(non-orthogonal) reference frame and the conserved quantities are rather
non-standard, yet at the same time quite intuitive to the problem at hand. Two
such problems are discussed in detail with two alternative approaches. The
first approach does not even require knowledge of calculus. In the appendix, I
also present the brute-force solution involving a coupled system of
differential equations. In addition, a few exercises and another similar
problem for students' "homework" are provided at the end.
