On May 18, 1999, at 1145 hours Pacific daylight time, a Cessna 172R, N9897F, sustained substantial damage during a hard landing at the Imperial, California, airport. Pinnacle Aviation in Palomar, California, was operating the instructional flight under the provisions of 14 CFR Part 91. The student pilot was completing the third leg of a solo cross-country flight. She departed Thermal, California, about 1125. Visual meteorological conditions prevailed and a VFR flight plan was filed. The pilot, the sole occupant, was uninjured. Inbound to Imperial, the pilot requested a landing advisory from Imperial Common Traffic Advisory Frequency (CTAF). They advised runway 14 was in use. As the pilot neared the airport, another aircraft asked for advisories. That aircraft was advised that runway 32 was in use and landed on it. The pilot tried to contact the CTAF to verify runway 32 was now in use, but received no response. She entered right traffic for runway 32 and noted the windsock indicated there was no wind. She overshot the turn to final but corrected to line up on the runway centerline. She flared too high and tried to correct; however, during the landing, the aircraft started to porpoise. The propeller struck the ground, buckling the cowling and firewall. The pilot taxied clear of the runway and shut down.