If end A of the rope moves downward with a speed if 5 m/s, determine the speed of cylinder b

Speed or angular speed? We need a better description of the situation.

To determine the speed of cylinder B, we need to consider the relationship between the rope and the cylinders. Since the rope is connected to both cylinders, their motion is interconnected. The key concept to understand here is that for an inextensible rope, the speed of both ends of the rope is the same. This means that the speed of end A of the rope, moving downward at 5 m/s, is also the speed of cylinder B.

So, the speed of cylinder B is 5 m/s.

To determine the speed of cylinder B, we need more information about the system and how the rope is connected to both cylinder A and cylinder B. Additionally, we need to know if there are any external forces acting on the system.

Please provide more details about the setup, such as the masses of cylinder A and B, the tension in the rope, any frictional forces, and how the rope is connected to both cylinders.