When Does m1's Velocity Become Zero or Negative After an Elastic Collision?

[Encarta]

Homework Statement

In an elastic collision, kinetic energy is conserved. That said, I do not have a specific question, but rather a broad, conceptual problem. Consider two similar masses of mass m. m1 approaches m2, with an initial velocity v1i and makes an elastic collision. Under what circumstances do the following cases happen?
a) m1's velocity after collision is zero.
b) m1's velocity after collision is in the negative direction (assuming it's initial path to be in the positive direction)?

Homework Equations

In an elastic collision, the difference between receding velocities is equal to the difference between approaching velocities of the masses.

The Attempt at a Solution

Given experience from playing pool and billiards, I would say that for a) to happen, the initial velocity of mass 2 has to be zero. This would also verify the "relevant equation" above.
For b, to happen, would the initial velocity of mass 2 have to be in the negative direction?

 

[xiaoB]

As i see if not going wrong, i would chose b) because the question has been said that is elastic collision. Except the question say is inelastic collision then i will chose a).

 

[Encarta]

Wait, sorry for not being clear, a and b are not options. They are two different scenarios. What would need to happen for a to take place? And what would need to happen for b to take place?