Final answer:
After the head-on collision, ball Y's velocity is 2 m/s in the same direction as ball X's initial velocity.
Step-by-step explanation:
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Since ball X stops after the collision, all of its initial momentum is transferred to ball Y.
Given that ball X has a mass of 1 kg and a velocity of 2 m/s, its initial momentum is calculated as:
Initial momentum of X = mass × velocity = 1 kg × 2 m/s = 2 kg·m/s
Since the total momentum after the collision is equal to the initial momentum of ball X, the momentum of ball Y is:
Final momentum of Y = 2 kg·m/s
Since the mass of ball Y is also 1 kg, its final velocity can be calculated as:
Final velocity of Y = Final momentum of Y / mass of Y = 2 kg·m/s / 1 kg = 2 m/s
Therefore, ball Y's velocity after the collision is 2 m/s in the same direction as ball X's initial velocity.