Kinematics of motion in a straight line — practice question

Particle $A$, with mass $0.2\,\text{kg}$, and particle $B$, with mass $0.6\,\text{kg}$, are joined to the two ends of a light inextensible string. The string passes over a fixed smooth pulley. $B$ is initially at rest $1.6\,\text{m}$ above the floor. $A$ hangs freely at a height of $h\,\text{m}$ above the floor. Both straight sections of the string are vertical (see diagram). $B$ is released and both particles begin to move. When $B$ reaches the floor it stays at rest, but $A$ continues moving vertically upwards until it is $3\,\text{m}$ above the floor.