I answered (a) then saw that you had already done that! Very good.

For (c), a "range" of values for

must have both an upper and lower bound. The upper bound is easy:

cannot be so large as to have no motion at all. The total force on the system is

(you must have calculated that when you did (a)) and the masses will not move if that is negative

leads to

. Now you are told that the mass A, which, as you calculated for (b) has speed

when B stops falling and so the only force on mass A is the friction force

. The acceleration due to that is

and that must stop A before it reaches the pulley.

A is initially distance 2h from the pulley. After B has fallen a distance h, A will have moved distance h also and so will be distance h from the pulley. Using decceleration

to determine the time required for A to stop. Calculate the distance A will have traveled. Find the value of

so that distance would be exactly h. That is the lower bound for

.