Question

Imagine two billiard balls on a pool table. Ball A has a mass of 2 kilograms and ball

Answer 1

1. The signs of the velocities of the balls were changed, this is a result of the elastic collision between the two balls. The law involved in here is the Law of Interaction.
2. During the elastic collision, the momentum is conserved. 
3. The velocity would be lower. There is a tendency for these balls to stick together. 

Answer 2

Explanation :

It is given that

mass of ball A $m_A=2\ Kg$

mass of ball B, $m_B=3\ Kg$

initial velocity of ball A, $u_A=9\ m/s$ (in right)

initial velocity of ball B, $u_B=-6\ m/s$ (in left)

final velocity of ball A, $u_A=-9\ m/s$ (in left)

final velocity of ball B, $u_A=6\ m/s$ (in right)

(1) After collision the velocities of balls gets exchanged.The velocity of ball A  and B will become 9 m/s and 6 m/s but in opposite direction.

This represents Newton's third law.

(2) Initial momentum,$p_i=m_Au_A+m_Bu_B$

$P_i=2\times 9+3\times -6$

$p_i=0$

Final momentum, $p_f=m_Av_A+m_Bv_B$

$p_f=2\times (-9)+3\times 6$

$p_f=-18+18=0$

So, this shows momentum is conserved.

(3) If masses and initial velocities of each ball were same, then $m_A=m_B=m$ and $u_A+u_B=u$

So, $2mu=m(v_A+v_B)$

$v_A=2u-v_B$  

and $v_B=2u-v_A$

This is required solution.