This has nothing to do with elastic collision, that is about the material of the colliding bodies?
https://en.wikipedia.org/wiki/Elastic_collision
If there were no inertia, then one object could not "crash into" another; it would bounce back by the angle of incidence = angle of reflection principle. No inertia = "massless" (effectively). And in Classical Physics it would by extension mean no momentum, regardless of velocity.
(Yes, E=mc^2 kicks in here with Quantum Mechanics and Relativity - meaning there would be energy, and hence some (small) inertia-mass from Kinetic Energy).
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