Do Balls X and Y Conserve Momentum and Energy in an Elastic Collision?

[Herzbog]

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

 

[Herzbog]

the picture is attached

 

[Doc Al]

What do you think? What can you say about elastic collision?

 

[Herzbog]

Ux- Uy = -Vx+Vy

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

 

[Doc Al]

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.)

 

[Herzbog]

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

 

[Herzbog]

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

 

[Doc Al]

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.