Final answer:
The momenta of the two carts remain unchanged just after the fans are turned off because the total momentum of a closed system is conserved when no external forces act on it. The scenario with carts A and B is an example of the conservation of momentum but not the conservation of kinetic energy, indicating an inelastic collision.
Step-by-step explanation:
The scenario describes two carts in a system where they undergo a collision and one of the carts comes to rest while the other moves away with some unknown velocity. The momenta of the two carts just after the fans are turned off will be as follows: a) They remain unchanged. Since no external forces are acting on the system, the total momentum of the system is conserved. This is in accordance with the conservation of momentum, which states that the total momentum of a closed system is constant if no external forces act on it.
For the collision described in the question, if object A is initially moving with a certain velocity and object B is at rest, and after the collision, object A comes to rest while object B moves with an unknown velocity, we can ascertain that b) Momentum is conserved, but since the objects experience a change in kinetic energy (object A stops and object B moves), kinetic energy is not conserved, making it an inelastic collision. This is clarified by the fact that object A, which had kinetic energy due to its movement, stops, indicating a transfer or loss of kinetic energy during the collision.