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`.

Explanation

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)))`