HISTORY OF FLIGHTOn January 16, 2015, about 1400 Hawaiian standard time, a Cessna 172N, N5660E, collided with terrain near Ualapue, on the Island of Molokai, Hawaii. The airplane was registered to Hawaiian Night Lights LLC, and operated by the pilot under the provisions of 14 Code of Federal Regulations (CFR) Part 91. The certified flight instructor (CFI), student pilot undergoing instruction, and one passenger sustained minor injuries; a second passenger sustained serious injuries. The airplane sustained substantial damage to the fuselage and both wings during the accident sequence. The instructional flight departed Honolulu International Airport, Honolulu, at 1304. Visual meteorological conditions prevailed, and no flight plan had been filed. The CFI reported that the flight was an introductory lesson for the student, who was a Japanese citizen, and that the student's parents were the passengers. The CFI was the owner of Hawaiian Night Lights, and utilized the airplane for flight instruction. The CFI stated that they planned to flying for 2 hours, and prior to departure, decided to fly east towards Molokai due to unfavorable weather conditions around the Island of Oahu. The departure was uneventful and they flew east, following the northern coastline towards the end of Molokai. Having reached a waterfall as they approached the eastern shore, the CFI took the controls and initiated a circling climb inland over the mountainous terrain. During the climb he noticed that the engine was not producing full power, even though the throttle control was fully forward. He estimated the engine speed to be about 200 rpm lower than normal, and he applied carburetor heat. The flight progressed over the mountains at an altitude of about 3,500 ft mean sea level (500 to 1,000 ft above ground level) while he maintained best rate of climb airspeed. As they passed over a ridge the airplane began to descend at 400 ft per minute, and they became trapped below the peaks of surrounding terrain. The pilot turned off carburetor heat and began performing tight turns and chandelle maneuvers in an effort to clear terrain while now flying at best angle of climb airspeed. He warned the passengers of the impending crash, however, as they did not speak English, they could not fully understand. As they approached the valley floor he extended the flaps and told the passengers to brace for impact. The airplane came to rest at the 3,000 ft level, on the eastern side of the island, 73 miles from the departure airport. Video of the accident site taken by search and rescue personnel revealed that the airplane was situated in densely wooded terrain within a crevasse just below a ridgeline. Due to the inhospitable nature of the terrain, the airplane could not be examined at the accident site. Additionally, the airplane was not insured, and at the time of completion of this report it had not been recovered from the accident site; therefore, no examination was performed. The most recent maintenance action performed on the airplane was an annual inspection, which was completed on August 1, 2014. According to maintenance logbooks, at that time the airframe had accrued 5,517.3 total flight hours, with the engine accumulating 1,362.7 hours since overhaul. The pilot reported that the airplane had flown an additional 95.6 hours since the inspection. Radar data provided by the FAA recorded the majority of the flight leading up to the turn towards terrain. The data revealed a target departing eastbound following the southeastern shoreline of Oahu. The target then made the 26-mile crossing over the Kaiwi Channel where it performed a series of turning maneuvers. It then continued to track along the northern shoreline of Molokai. The final segment of the flight was not recorded as the airplane descended behind terrain and out of the radar coverage area.