Newton's laws of motion — practice question

A light inextensible string has one end attached to particle $A$ of mass $3\,\text{kg}$, while the other end is connected to particle $B$ of mass $4\,\text{kg}$. Particle $A$ is on a rough plane inclined at $30^\circ$ to the horizontal, and particle $B$ is on a smooth horizontal plane. A second light inextensible string is joined to $B$; its other end is attached to particle $C$ of mass $5\,\text{kg}$, which hangs vertically. Both strings are taut and pass over small smooth pulleys fixed at the ends of the horizontal plane. The segment of string from $A$ to the pulley is parallel to a line of greatest slope of the inclined plane, and $A$, $B$ and $C$ all lie in the same vertical plane (see diagram). The system is released from rest. In the motion that follows, $C$ moves vertically downwards with acceleration $2\,\text{m s}^{-2}$, and neither $A$ nor $B$ reaches a pulley.