Which method allows for rapid mooring to a buoy by letting the chain slide on the wire shackled to the buoy?

The correct method for rapid mooring to a buoy by allowing the chain to slide on the wire shackled to the buoy is the trolley system. A trolley is designed to facilitate the movement of mooring lines or chains effectively. When mooring to a buoy, the ability of the trolley to allow the chain to slide means that the vessel can quickly adjust to changes in position without the need for extensive manual adjustments to the chain, promoting a smoother and faster mooring process.

In contrast, the bollard serves primarily as a stationary fixture for securing the mooring line but does not provide the sliding capability necessary for rapid adjustment. The capstan is typically used for handling lines but does not inherently allow for the sliding motion associated with docking operations at a buoy. Lastly, while a pulley can redirect or change the angle of a line, it does not specifically facilitate the rapid sliding motion necessary for this particular mooring technique. Thus, the trolley is the best fit for the described scenario.