Question

A bucket with mass m = 1.0 kg is suspended over a well by a winch and rope. The winch consists of a solid cylinder with mass 4.0 kg and radius R = 0.10 m about which the rope is wrapped. A handle is attached to one end in order to rotate the cylinder. For the purposes of this example, we are going to ignore any frictional forces in the winch. Now suppose that the winch handle breaks off, allowing the bucket to fall to the water as the rope unwinds from the cylinder. Assume that the bucket is released at t=0 and the water level is at a depth h = 2.2 m below the bucket at t=0. How far above the water is it at 0.50 s?

1.8 m (with sig figs) is the correct answer but I would like to know how to get this answer

Answer 1