The Cay by Theodore Taylor explores the relationship between Timothy, "an extremely old...yet powerful black man" and Phillip, a young American returning to the USA with his mother. The two form a bond and a sincere friendship during their harrowing experiences, afloat in the ocean on a raft and reliant on Timothy's ability to steer them to safety with little water and only his wits to guide him.
The sinking of the ship on which Timothy and Phillip are travelling is not necessarily the main climax of the story and contributes more to the rising action because the story revolves around the fight for survival as Phillip and Timothy find themselves drifting in the ocean with no sign of rescue. They are unaware of the fate of the ship although Timothy does all he can to allay Phillip's fears about his mother's whereabouts.
The two struggle against the forces of Nature and Timothy makes the decision to make their way onto dry land, despite his concerns that this may in fact hamper their rescue. On the island, they begin to make the best of their time there, Phillip even eventually managing to retrieve some coconuts and Timothy making provision for a blind Phillip to manage if he is left alone.
The climax comes as the weather (Nature) builds and a hurricane hits the island. As it subsides, Phillip realizes that Timothy is "cold and limp," although he is not dead. He sits with Timothy, powerless to help him recover and falls asleep. The falling action then is represented as the plot unfolds after the storm. Phillip begins to appreciate all the effort that Timothy made so that he could survive until rescue arrived. Stew Cat returns and Phillip is relieved that he is not completely alone. Phillip even perfects his fire when he realizes that the only way to make his presence known to the aircraft is to send a recognizable signal with black smoke. Later, the reader is told that the aircraft had radioed to the Destroyer (ship) which comes to rescue Phillip.
There are other potential points at which the story turns and it depends on your interpretation. As long as you support your answer, you may wish to choose other significant events which also involve a potential turning point and from which the falling action ensues or follows.