Final answer:
The billiard ball collision described cannot be a perfectly inelastic collision since both balls move after the impact and not together as one body. Since kinetic energy is not conserved, it is not a perfectly elastic collision either. The collision is, therefore, a partially inelastic collision.
Step-by-step explanation:
The question is asking to determine the type of collision between two billiard balls, based on the information provided about their velocities before and after the impact. To analyze the nature of the collision, we can use the principles of momentum conservation and kinetic energy conservation.
Firstly, we should note that in an elastic collision, both the conservation of momentum and the conservation of kinetic energy apply. This means that the total kinetic energy before and after the collision remains the same. On the other hand, in an inelastic collision, only the momentum is conserved, while kinetic energy is not conserved.
In a perfectly inelastic collision, the two objects stick together after the collision, moving with the same final velocity. The fact that, in this question, both balls are moving separately after the collision eliminates option b, the perfectly inelastic collision. Since the first ball slows down after the collision, it suggests that some kinetic energy is lost, ruling out a perfectly elastic collision (option a).
Therefore, without additional information to calculate the kinetic energies post-collision, we can conclude that the collision is a form of partially inelastic collision, which means that there is some loss of kinetic energy but the objects do not stick together. This leads us to select options c and d, partially elastic or partially inelastic collisions, as the likely answers.
The exact classification between partially elastic and partially inelastic would require further analysis of the kinetic energy before and after the collision, which cannot be determined from the given information alone.