All surfaces are smooth. Find the horizontal displacements of the block and 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))` = constant
`vec(P_(f))=vec(P_(i))` (along x - axis) `" " m vec(u)+M vec(V)=vec(0)`
`x_(1)=` forward distance moved by the block along x - axis.
`x_(2)=` backward distance moved by the wedge along x -axis.
`m vec(u)=-M vec(V), m (x_(1))/(t)=M(x_(2))/(t)`
`mx_(1)=Mx_(2) " " x_(1)=(ML)/(M+m)=(M l cos theta)/(M+m)`
`x_(2)=(mL)/(M+m)=(ml cos theta)/(M+m)`
L can also be written as `l cos theta`.