In a perfectly inelastic one-dimensional collision between two objects, what initial condition alone is necessary so that all of the original kinetic energy of the system is gone after the collision

The objects must have moments with the same magnitude but opposite directions.

Explanation:

The condition alone that is necessary in order to make the final kinetic energy of the system to be zero after the collision is that the objects must have moments that are the same in magnitude but have opposite directions.

d.7.5cm is your answer