Question

Two identical billiard balls of diameter 5 cm, each moving with a speed of 3 m s$^{-1}$, roll, without slipping, towards each other on a horizontal rectangular U-shaped trough that is sufficiently deep that the balls are clear of its base (see figure). The resulting instantaneous collision is perfectly elastic, and, during it, each ball reverses its linear velocity, though their angular velocities are not affected. How wide does the trough need to be approximately for balls to collide twice?

Answer 1

Unknown

Answer 2

This is a very complex problem that requires more information to solve. A complete solution would require a detailed analysis of the geometry of the trough, the coefficient of restitution of the collisions with the sides of the trough, and the length of the trough. Without these details, it's impossible to determine the width needed for a second collision.