A particle of mass m_(1) is projected to the right with speed v_(1) onto a smooth wedge of mass m_(2) which is simulateoulsy projected due the left with a speed v_(2). If the particle attains the highest point of the wedge, find h.

A particle of mass m_(1) is projected to the right with speed v_(1) on

1.	A particle of mass m_(1) is projected to the right with speed v_(1) onto a smooth wedge of mass m_(2) which is simulateoulsy projected due the left with a speed v_(2). If the particle attains the highest point of the wedge, find h.
Answer» Solution :Applying work energy THEOREM `W_("TOTAL")=/_\K_("blocks",cm)+/_\K_(cm)` As no external forces ACTING, the velocity of centre of mass will be constant. Hence `/_\K_(cm)=0` Hence `W_("total")=/_\K_("blocks",cm)` `W_("gravity")=[1/2muv_(rel)^(2)]_("final")-[1/2muv_(rel)^(2)]_("initial")` `-m_(1)gh0-1/2((m_(1)m_(2))/(m_(1)+m_(2)))(v_(1)+v_(2))^(2)` `-m_(1)gh=-1/2((m_(1)m_(2))/(m_(1)+m_(2)))(v_(1)+v_(2))^(2)` `h=1/2(m_(2)(v_(1)+v_(2))^(2))/(g(m_(1)+m_(2)))`