In "The Most Dangerous Game" how is Rainsford separated from the yacht?

At the beginning of "The Most Dangerous Game" the reader finds Rainsford, the protagonist, on the deck of a yacht with his good friend, Whitney. Rainsford is headed to Rio with his friend to hunt in the Amazon. The story opens on the men discussing the island that they are currently passing. Whitney tells Rainsford that the island is known to sailors as an unlucky place nicknamed "Ship Trap Island." 

The men briefly discuss hunting (foreshadowing), the weather (it's foggy and difficult to see), and how the boat's crew is superstitious regarding the island (the crew has been unusually silent all day). When Whitney heads to bed, Rainsford decides he's going to stay up a while longer to smoke another pipe.

While relaxing on deck, Rainsford hears a gunshot in the distance. An experienced hunter, his curiousity is piqued by the fact that the island is supposed to be uninhabited. Moving quickly and without thinking, Rainsford jumps up onto the railing in an attempt to get a better view. Unfortunately, he loses his pipe in the process and in lunging to try to recover it, falls overboard. As it's the middle of the night, Rainsford can't attract anyone's attention from the boat itself, so he begins to swim to shore.