I just thought it would make more sense if I showed a picture of exactly what I didharuspex said:
A perfectly elastic collision is a type of collision in which the total kinetic energy of the system is conserved. In other words, the total energy before and after the collision is the same. This means that there is no loss of energy due to heat, sound, or deformation.
In a perfectly elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the energy is lost due to heat, sound, or deformation. In an inelastic collision, the objects stick together after the collision, while in a perfectly elastic collision, the objects bounce off each other.
The equations used to solve a perfectly elastic collision problem with no given values are the conservation of momentum equation and the conservation of kinetic energy equation. These equations can be used to find the final velocities of the objects involved in the collision.
In theory, a perfectly elastic collision can occur in real life, but in reality, it is nearly impossible to achieve. This is because there will always be some energy lost due to factors such as friction and air resistance. However, some collisions, such as collisions between subatomic particles, can be considered perfectly elastic.
The main limitation of solving a perfectly elastic collision problem with no given values is that it assumes an ideal scenario where there is no energy lost due to external factors. In reality, there will always be some energy lost, so the solutions obtained may not be entirely accurate. Additionally, if there are more than two objects involved in the collision, the problem becomes more complex and difficult to solve without given values.