At the instant shown, the center O of a spool with inner and outer radii r = 3 ft and R =...

At the instant shown, the center O of a spool with inner and outer radii r = 3 ft and R = 7 ft, respectively, is moving down the incline at a speed υO = 12.2 ft/s. If the spool does not slip relative to the rope and if the rope is fixed at one end, determine the velocity of point C (the point on the spool that is in contact with the incline) as well as the rope’s unwinding rate, that is, the length of rope being unwound per unit time.

Figure P6.54