What is the relationship between impact parameter and billiard ball collisions?

[ordinarydaysx]

Homework Statement

My problem has to do with impact parameter of two billiard balls. I don't want my problem solved persay, I just want to understand the problem, as I have a few things I am unclear about. If impact parameter is what "would've been the distance of the closet approach of the centers" doesn't that just mean it's the distance between the two centers if the balls were together? And when given the impact parameter, how do I approach a problem that asks us to find the angle the balls were at when they hit?

Homework Equations

The Attempt at a Solution

 

[wdednam]

Hi,

Say the two billiards balls are on a collision course with one another, so that their lines of motion are parallel but do not necessarily coincide. The impact parameter is the perpendicular distance between their parallel lines of motion.

If they were to collide head-on, and their initial lines of motion were parallel, then the impact parameter would be zero because their lines of motion now coincide. But the distance of closest approach would not be zero:

The distance of closest approach for a collision between two billiard balls is the distance between their centres when they are touching. If they don't actually collide, then the impact parameter becomes the distance of closest approach if their lines of motion are parallel.

Hope this helps.