Object A stays between a wall and object B. Object B moves with velocity V to collide with object A. Count the times of collision between object A and B, and between object A and the wall.
wall
|
|
| A v B
| o <-- O
The mass of B is 100^n times of A's mass. Then the bounce times become Pi x 10^n.
n bouncing-times
0 3
1 31
2 314
3 3141
4 31415
5 314159
6 3141592
7 31415926
8 314159265
This can be proven in math.
One way to prove it is to treat the velocities (with direction) of Va and Vb as the cordinate (x, y) of a point on a circle, based on the law of kinect energy conservation in elastic collision. I will put here a solution when I can spare some time.