Final answer:
The final velocity of the third ball in the closed system is 8 m/s.
Step-by-step explanation:
To find the velocity of the third ball in this closed system, we can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system, assuming no external forces act on the system. Since the first ball is at rest before the collision and after collision, we can calculate the momentum of the system before the collision using the mass and velocity of the second ball. The momentum of the system after the collision is the same as the momentum of the second ball before the collision, as the third ball was initially at rest. So, we have:
Momentum before collision = Momentum after collision
(Mass of ball 2) × (Initial velocity of ball 2) = (Total mass of balls 2 and 3) × (Final velocity of ball 2)
Plugging in the values: (0.6 kg) × (12 m/s) = (0.6 kg + 0.2 kg) × (Final velocity of ball 2)
Simplifying, we get: Final velocity of ball 2 = (0.6 kg × 12 m/s) / (0.6 kg + 0.2 kg)
Calculating, the final velocity of ball 2 is 8 m/s.