On January 27, 2002, about 1140 eastern standard time, a Cessna 172R, N9525V, was substantially damaged while landing at the Chesterfield County Airport (FCI), Richmond, Virginia. The student pilot was not injured. Visual meteorological conditions prevailed for the instructional flight that departed the Charlottesville-Albemarle Airport (CHO), Charlottesville, Virginia, destined for Chesterfield. A visual-flight-rules flight plan was filed and activated for the flight conducted under 14 CFR Part 91. The student was returning from her first cross-country solo flight. She entered a downwind for runway 15 about midfield. Because she was following another airplane, she extended the downwind for spacing. She turned base and then final a "little faster than normal," but had extra time from extending the downwind. She slowed the airplane to approximately 65 to 70 knots, and selected 30 degrees of flaps. While concentrating on descent angle, airspeed, and maintaining centerline alignment, the student "did not flare properly," and the airplane touched down hard. The airplane bounced back into the air, and then touched down three more times. The student does not remember pushing the yoke forward during any of the bounces, but felt the airplane may have touched down nose wheel first. The student taxied to parking, and the airplane was placed in its hangar. According to a Federal Aviation Administration inspector, the propeller displayed ground impact damage. He also observed damage to the nose wheel assembly, and several compression wrinkles on the engine firewall.