= θ = , we regain Eq. ( . ) for one dimensional collision. If, further the collision is elastic, ( .
) We obtain an additional equation. That still leaves us one equation short. At least one of the four unknowns, say θ , must be made known for the problem to be solvable. For example, θ can be determined by moving a detector in an angular fashion from the x to the y axis.
Given { m , m , v 1i , θ } we can determine { v 1f , v 2f , θ } from Eqs. ( . )-( . ).
Example . Consider the collision depicted in Fig. . to be between two billiard balls with equal masses m = m .
The first ball is called the cue while the second ball is called the target. The billiard player wants to ‘sink’ the target ball in a corner pocket, which is at an angle θ = °. Assume that the collision is elastic and that friction and rotational motion are not important. Obtain θ .
Answer From momentum conservation, since the masses are equal 2f 1f 1i or