Two particles of equal mass m have respective initial velocities  ui^ and ui^+j^2 . They collide completely inelastically. The  energy lost in the process is :

Applying Momentum Conservation,  m1u→1+m2u→2 = (m1+m2)V→c ⇒m(ui^)+mu(i^+j^2)=2mV→c ⇒V→c =34ui^+14uj^ Now, magnitude of the speeds are,  u1=u u2=u2 Vc=104u  K.E loss =Ki−Kf ⇒K.E loss = (12m1u12+12m2u22)−12(m1+m2)Vc2                       =(12mu2+12mu22)−12(2m)1016u2                       =18mu2