Two particles P and Q, of masses 0.3 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a smooth plane. The plane is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac{3}{5}\). P lies on the plane and Q hangs vertically below the pulley at a height of 0.8 m above the floor (see diagram). The string between P and the pulley is parallel to a line of greatest slope of the plane. P is released from rest and Q moves vertically downwards.

1. Find the tension in the string and the magnitude of the acceleration of the particles. [5]
2. Q hits the floor and does not bounce. It is given that P does not reach the pulley in the subsequent motion.
3. Find the time, from the instant at which P is released, for Q to reach the floor. [2]
4. When Q hits the floor the string becomes slack. Find the time, from the instant at which P is released, for the string to become taut again. [4]