On May 3, 1998, about 1400 eastern daylight time a Cessna 172P, N54743, collided with rough terrain during a touch and go landing at the Key West Airport, Key West, Florida. The airplane was operated by the student pilot under the provisions of Title 14 CFR Part 91, and visual flight rules. Visual meteorological conditions prevailed and no flight plan was filed for the local instructional flight. The student pilot and sole occupant was not injured and the airplane sustained substantial damage. The flight had originated about 10 minutes prior to the accident. According to the student pilot, while practicing touch and go landings, he landed long and departed the left side of runway 09 at the 2000 foot marker, and encountered rough terrain, substantially damaging the airplane. The student pilot stated that he had accumulated 25 hours total time, and 3.7 hours in a Cessna 172. According to the FAA inspector, the student pilot had not received sufficient training in the 172.