  Analysis of collisions is standardly included in the introductory physics
course. In one dimension (1D), there do not seem to be any unusual issues:
Typically, the initial velocities of the two colliding objects are specified,
and the problem is to find the final velocities. In 1D there are therefore two
unknown variables. One can write the equation for conservation of momentum, and
either the equation for conservation of energy for the perfectly elastic case,
or the expression for the coefficient of restitution (COR) otherwise. Thus, one
has two equations for two unknowns, and one may solve the problem fully. An
issue arises, however, in two-dimensional (2D) collisions: There are four
unknown variables (two components of the final velocity of each object), but
now there appear to be only three equations: two components of the equation of
conservation of momentum, and the energy condition. The problem may appear
therefore to be underdetermined. If this problem were in principle an
underdetermined one, one would fail in predicting the outcome of the collision
experiment. We describe how one may assign students an appropriate lab exercise
and problems for an interesting class of 2D collisions for which one can
determine uniquely the outcome of the collision.
