Probability of puck bouncing of wald

[whoelsebutme]

There is a rectangular surface with no friction, and a puck with no friction on its bottom surface sits at a random point on this surface. This puck is now given a push in a random direction. The walls of the surface all have coefficient of restitution of 1, so the puck will bounce off the walls forever at the same speed.

What is the probability that the puck will eventually pass through the same point, moving in the same direction ?

 

[GENIERE]

100% -

 

[actionintegral]

If you are dealing with a continuum, you need a probability density. That is, probability per unit area of occupying a point, and probability per unit angle of having the given velocity.