Particles $A$ and $B$, of masses $0.9{\text{ }}kg$ and $0.6{\text{ }}kg$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley. The system is released from rest with the string taut, with its straight parts vertical and with the particles at the same height above the horizontal floor. In the subsequent motion, $B$ does not reach the pulley.
a) Find the acceleration of $A$ and the tension in the string during the motion before $A$ hits the floor.
After $A$ hits the floor, $B$ continues to move vertically upwards for a further $0.3{\text{ }}s$.
b) Find the height of the particles above the floor at the instant that they started to move.
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