Answer:
in the positive x-direction.
Explanation:
Conservation of momentum tells us that the momentum before the collision must be equal to the momentum after the collision: .
Before the collision we have:
And after the collision:
Since they must be equal we have:
Which is the same as:
And can be written as:
Since the collision is elastic, kinetic energy is conserved:
Before the collision we have:
And after the collision:
Since they must be equal we have:
Which is the same as:
And can be written as:
Which is the same as:
But since we already proved that , we can cancel those terms and we have that:
So we have the system:
Adding both sides between them we obtain:
Which is:
Which means:
Where we used a positive velocity since ball 1 travels in the positive x-direction at the beginning.