Let V be the velocity of body Q after the collisions. From the principle of conservation of linear momentum, we have mu = mυ + (2m) V or u - υ = 2V (1) The conservation of kinetic energy gives
1
2
mυ2 =
1
2
mυ2 +
1
2
(2m)V2 Or u2−υ2 = 2V2 (2) Using Eq (1) in Eq (2), we have Or 2 (u + υ) = 2V (3) From Eqs. (1) and (3), we get V = -u/3. Using v =-u/3 in Eq. (1), we get V = 2u/3.