Loads $A$ and $B$, of masses $1.2{\text{ }}kg$ and $2.0{\text{ }}kg$ respectively, are attached to the ends of a light inextensible string which passes over a fixed smooth pulley. $A$ is held at rest and $B$ hangs freely, with both straight parts of the string vertical. $A$ is released and starts to move upwards. It does not reach the pulley in the subsequent motion.

a) Find the acceleration of $A$ and the tension in the string.

b) Find, for the first $1.5$ metres of A’s motion,

(i) A’s gain in potential energy,

(ii) the work done on $A$ by the tension in the string,

(iii) A’s gain in kinetic energy.

$B$ hits the floor $1.6$ seconds after $A$ is released. $B$ comes to rest without rebounding and the string becomes slack.

c) Find the time from the instant the string becomes slack until it becomes taut again.