# Momentum of two balls

Two balls X and Y collide elastically. Their speeds before and after collision are as shown.
Before

After
Which of the following equations is correct?

A Ux +Uy = Vx +Vy
B Ux +Uy = Vx - Vy
C Ux - Uy = Vx +Vy
D Ux - Uy = Vx - Vy

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Doc Al
Mentor
What do you think? What can you say about elastic collision?

Ux- Uy = -Vx+Vy

Ux- Uy = -Vx+Vy
I think this is the right equation.

Doc Al
Mentor
Why? What's your reasoning? What physics principle or result are you appealing to? (Hint: The directions of the velocities are given; Treat the U's and V's as positive numbers.)

The conservation of momentum.
It is elastic collision. Overall speeds are equivalent before and after the collision.

Let the direction of Ux be positive and thus that of Vx is negative.

Doc Al
Mentor
The conservation of momentum.
It is elastic collision.
Good.
Overall speeds are equivalent before and after the collision.
I don't know what this means. Hint: Conservation of momentum and energy leads to a very specific conclusion about velocities before and after the collision.

Let the direction of Ux be positive and thus that of Vx is negative.
OK.