Two particles P and Q are attached to opposite ends of a light inextensible string which passes over a small smooth pulley at the top of a rough plane inclined at 30° to the horizontal. P has mass 0.2 kg and is held at rest on the plane. Q has mass 0.2 kg and hangs freely. The string is taut (see diagram). The coefficient of friction between P and the plane is 0.4. The particle P is released. Q strikes the floor and remains at rest. P continues to move up the plane for a further distance of 0.8 m before it comes to rest. P does not reach the pulley. Find the speed of the particles immediately before Q strikes the floor.
For this question I need to set 0.2a = 0.2gsin30 + 0.4x0.2gcos30. I don't really understand why we need to do this. Why couldn't I just use these simultaneous equations 0.2g - T = 0.2a and 0.2a = T- 0.2gsin30 -0.4x0.2gcos30? (The mark scheme says that this problem cannot be solved using these equations, but I don't understand why).