Would the 2 items displayed in the image below act as I expect in a zero G environment? Would they retreat away from one as depicted (assuming contact at 45 degrees)

 

Assuming that item A had a mass of 100kg and was stationary, Items B have a mass of 1kg and travel at 10m/s.

 

what formula would I need to use to calculate the velocities and vectors of the items after a collision?

 

You would use conservation of momentum, and, if the collisions are elastic, conservation of kinetic energy.

So Kinetic energy of the items just prior to collision would be;

 

Item A = 0 Joules

Items B = 50 Joules

 

and momentum;

 

Item A = 0 kg-m/s

Items B = 10 kg-m/s

 

and momentum After the collision;

 

Item A = 0.19802 kg-m/s

Items B = -9.80198 kg-m/s

 

Is that correct? what vectors would the momentum be carried?

The momentum of the system is zero, since momentum is a vector. Each ball has a momentum of 10 kg-m/s, but the signs are opposite. So after the collision, the balls moving down and the frame moving up will have equal momentum magnitudes.

 

The balls each have a KE of 50J, so the total is 100J.