Such problems are usually solved most easily using conservation of energy.
Before A hits the ground both strings remain taut. The distance B moves is half the distance A moves, and the speed of B is half that of A. The speeds of A and B at any time can be related to the angular velocity of the pulley, assuming there is no slipping between strings and pulley.
So you can write that at any instant before A hits the ground :
(PE lost by A) = (KE gained by A, B and pulley) + (work done against friction by B).
When block A hits the ground its KE is dissipated as heat and sound so it is removed from the system. The KE which remains in the system equals the further work done against friction by block B, because the system is finally at rest and the only way that the KE in the system can be dissipated is by friction at B. This allows you to find the distance B moved after A hit the ground.
Add the distance moved by B before A hit the ground (0.5m) to the distance it moved after.