Forces and equilibrium — practice question

The diagram depicts a triangular block whose sloping faces make angles of $45^{\circ}$ and $30^{\circ}$ with the horizontal. Particle $A$, with mass $0.8\text{ kg}$, is on the face inclined at $45^{\circ}$, while particle $B$, with mass $1.2\text{ kg}$, is on the face inclined at $30^{\circ}$. The particles are joined by a light inextensible string that passes over a small smooth pulley $P$ fixed at the top of the faces. The segments $AP$ and $BP$ of the string run parallel to the lines of greatest slope on the respective faces. The particles are let go from rest with both parts of the string taut. During the ensuing motion, neither particle reaches the pulley and neither one reaches the bottom of a face.