The monkeys and bears decided that since Hanuman was the son of the Wind God, Vyu, he was the best at jumping and must leap to Lanka. Hanuman had his father's energy and swiftness, power and strength. (When Hanuman was a child he thought the sun was a ripe fruit and tried to jump up and catch it. He jumped so high that he nearly got burnt, but the Sun was impressed and gave Hanuman the gift of immortality as a reward for his courage and cleverness.)
Rama gave Hanuman his ring, to give to Sita. Hanuman prayed to his father and jumped. (Hanuman's leap is the subject of many paintings.) Hanuman leapt over the ocean, escaping several devouring demons that he met on the way. Here you can see him jumping through the jaws of Surasa, a sea monster, on the way to the island of Lanka.