On March 2, 2005, about 1255 central standard time, a Cessna 172, N212CF, registered to KEMS LLC and operated by Madison Flyers, as a Title 14 CFR Part 91 instructional flight, had a hard landing at the Bruce Campbell Field Airport, Madison, Mississippi. Visual meteorological conditions prevailed and no flight plan was filed. The student pilot received no injuries, and the airplane incurred substantial damage. The local flight originated earlier that day, about 1100. The student pilot stated that after returning to Bruce Campbell Field the certified flight instructor (CFI) permitted her to conduct several solo flights. On her third landing, the airplane was within 10 feet of the ground when she flared. At this point, she felt a strong gust of wind and the airplane began to "balloon" back up. She attempted to maintain the airplane level to touch down, but it hit the runway and began to porpoise back up, as she attempted to maintain control. The airplane hit the runway hard again, she applied the brakes and proceeded to turn off at the taxiway but she felt like the airplane was a little "out of control," unable to control the turn, the left wheel went into the grass. Once stopped she radioed for the assistance of the CFI. The student pilot stated there were no mechanical failures or malfunction to the airplane or any of its systems prior to the accident. The CFI stated that after returning to Bruce Campbell Field he had the student pilot stop and drop him off so she could perform several solo flights. He told her to fly multiple touch and goes and that he would listen for her on his hand held radio. He was only in the fixed based operators office for a short time when he was advised his student had the airplane in the grass. He then went out to the airplane and assisted the student by taxing the airplane back to the ramp. The responding FAA accident inspector stated the student pilot was conducting her third solo landing when it appeared to her the landing was going to be long. She then pushed the airplane on down to the runway until it hit. Then it bounced back up hitting the runway much harder knocking her headset off. She regained control enough to keep the airplane from going all the way off the runway. After coming to a stop with the left wheel in the grass she called the fixed based operator and the CFI came out to aid her. The CFI stated he taxied the airplane back to the ramp and shut it down. Inspection of the airplane revealed approximately 12 1/2 inches of the firewall to be creased. The airplanes belly and floor also had creases. The ailerons operated normally but, the elevator yoke was binding only on the pilots control column. The bracket holding the yoke was observed to be bent, from impact forces.