# Rigid bodies - force to target calculation help

I’m having a bit of a physics problem that I need some help with.

The set up:
I have several rigid bodies (circles in this example) in a 2D friction environment. Thus I only need to worry about x and y calculations. All of the circles are aware of each other and can collide. All they have to do is reach a target with a fair degree of accuracy. However, since they collide, their vectors may deviate from the intended target.

The problem:
What I need to accomplish is applying a force to these targets to make them move from rest to a target given a constant friction force. Since they can collide, simple easing functions aren’t going to cut it since their vectors will change.

For example, think of throwing several billiard ball down the table. Only you have absolute certainty where they will land as long as no other ball interacts with it.

How would you be able to calculate how much velocity should be applied to counter friction and reach the target? Any pointers would be of great help.