# 2D kinematic motion collision

This is not for an assignment as much as my own edification, but as it is a homework-style question, I thought this would be the best place. If not, I apologize.

## Homework Statement

Given two hockey pucks of radius R1 and R2 on a frictionless, infinite level plane, located at (X1,Y1) and (X2,Y2) and moving at constant velocities (Vx1,Vy1) and (Vx1,Vy1) respectively:

1) Determine whether or not the two pucks will ever collide.
2) How long in seconds until they collide?

## Homework Equations

D = ([X1-X2]2+[Y1-Y2]2)
dX = Vx*dt
dY = Vy*dt

## The Attempt at a Solution

It seems obvious to start at figuring out if they are currently colliding, which is if the distance between them is less than their combined radii: D = ([X1-X2]2+[Y1-Y2]2) < (R1 + R2)

So I need to figure out how the position and velocity can be fit into this. I know the kinematic equations for position with respect to velocity and time are dX = Vx*dt and dY = Vy*dt, but I can't seem to figure out where to go next. It seems like it should be simple.

Last edited:

Spinnor
Gold Member
Come up with the equations for the pucks centers as a function of time. These functions define two straight lines in 2D spacetime. Now Google "distance between two lines" for formulas that determine the distance between two lines. If the minimum distance is less then r_1 + r_2 then they collide?

Or just let them move small steps in time and calculate the distance between centers. A short computer program could do this.