Imagine two billiard balls on a pool table. Ball A has a mass of 7 kilograms and ball

Question

B has a mass of 2 kilograms. The initial velocity of the ball A is 6 meters per second
to the right, and the initial velocity of the ball B is 12 meters per second to the left. Compare the final velocity of the balls.

Answer 1

Momentum conservation applies, as does Energy.
Momentum
7*6+2*(-12)=7Va+2Vb
Energy
7/2*6^2+2/2*(-12)^2=7/2 * Va^2+2/2*Vb^2

now on first equation, solve for either of the velocity (I will do Va)
7Va=-2Vb+42-24
Va= you do that.
Now, put that term on the right into the energy equation for Va, and solve for Vb. A bit of algebra will be required, so allow yourself some blank paper.
Once you get Vb, go back and solve for Va.
Then compare them.

Answer 2

Given:
M1 = 7kg, V1 = 6 m/s.
M2 = 2kg, V2 = -12 m/s.
V3 = ? = Velocity of M1 after collision.
V4 = ? = Velocity of M2 after collision.

Momentum before = Momentum after:
M1*V1 + M2*V2 = M1*V3 + M2*V4.
7*6 + 2*(-12) = 7*V3 + 2*V4,
Eq1: 7V3 + 2V4 = 18.

Conservation of KE Eq:
V3 = (V1(M1-M2) + 2M2*V2)/(M1+M2).
V3 = (6(7-2) + 4*(-12))/(7+2),
V3 = (30 -48)/9 = -2 m/s.
In Eq1, replace V3 with -2 and solve for V4.