Final answer:
In an inelastic collision involving an isolated system, the final total momentum is exactly the same as the initial momentum, according to the law of conservation of momentum. Option A is the correct answer.
Step-by-step explanation:
In the context of an inelastic collision involving an isolated system, the principle of conservation of momentum states that the total momentum remains constant when no external forces are involved.
This means that, regardless of the internal changes that happen during the collision, such as changes in kinetic energy, the final total momentum of the system will be the same as the initial momentum.
This principle is illustrated when two objects of equal mass are involved in a one-dimensional inelastic collision; if one is at rest and the other is in motion, after the collision, the combined mass will move with a certain velocity that ensures the conservation of momentum.
When two objects collide in elastically, they may stick together, as described in the given example with two air cars with putty, creating a perfectly inelastic collision.
While kinetic energy, the energy associated with motion, is not conserved in inelastic collisions (it is transformed into other forms of energy like heat or sound), momentum is always conserved.
To expand on the example provided, if cart A is moving and collides with cart B which is at rest, and they stick together post-collision, they will both move at a velocity that is half of cart A's initial speed. This ensures the momentum before and after the collision is equal.
Therefore, considering the conservation of momentum in inelastic collisions, the answer to the student's question is: (a) exactly the same as the initial momentum.