Why Velocity Same at Min Separation? | Conservation of Momentum

[EgpYo]

Homework Statement

Why is the velocity the same at minimum separation?
For example, two positively charged pucks are traveling towards each other. Find the minimum separation.

They oppose each other so they should slow down and reach minimum separation when their velocities are 0. It does not make sense to solve for when their velocities are the same. Because I get an answer of 1.0m/s, but how can they be at minimum separation if they are still moving?

Homework Equations

Conservation of momentum

The Attempt at a Solution

Use conservation of momentum to solve for the velocity. This is what the book says, but why? Shouldnt the minimum distance be when both of their velocities are 0?

 

[gneill]

Much depends upon the frame of reference used to judge what the velocities are, what the initial speeds of the pucks are (are they different?), the masses of the pucks (are they different?). While minimum separation will take place when the relative velocity of the pucks is zero, the two may still have some nonzero velocity in the lab frame of reference.