Final answer:
When the skaters push each other apart, they exert equal and opposite forces on each other. After they separate, the momentum and velocity of each skater can be determined using their mass and initial velocity. The total momentum of the skaters just after separation can be calculated by summing up their individual momenta.
Step-by-step explanation:
When the skaters push each other apart, they exert equal and opposite forces on each other. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that the force the 60 kg skater exerts on the 80 kg skater is the same magnitude as the force the 80 kg skater exerts on the 60 kg skater, but in the opposite direction.
After they separate, the momentum of each skater can be calculated using the equation momentum = mass × velocity. The 60 kg skater's initial horizontal velocity is given as 4.00 m/s, so their final velocity after separating can be determined by dividing their momentum by their mass. The same calculation can be done for the 80 kg skater.
Since momentum is a vector quantity, the direction of each skater's velocity after separation will be opposite to the direction of the force applied during the push. The magnitude of each skater's velocity will depend on their initial momentum and mass.
Their total momentum just after they separate can be calculated by summing up the momentum of each skater. The total momentum will be conserved unless external forces act on the system.