All surfaces are smooth Find the horizontal displacements of the block and the wedge when the block slides down from top to bottom
.

Explanation

When the block slides down on the smooth wedge, the wedge moves backwards. In the horizontal direction there is no external force , `vec(F_(x))=0`
`therefore vec(P_(x))="consant"`
`vec(P_(f))=vec(P_(i))" (along x - axis), "m vecu+MvecV=vec0`
`x_(1)=` forward distance moved by the block along X - axis.
`x_(2)=` backward distance moved by the wedge along X - axis.
`m vecu=-MvecV`,
`m(x_(1))/(t)=M(x_(2))/(t)`
`mx_(1)=Mx_(2), x_(1)=(ML)/(M+m)=(Mlcos theta)/(M+m)`
`x_(2)=(mL)/(M+m)=(ml cos theta)/(M+m)`