On the student pilot's first supervised solo flight; she reported that on her first landing the airplane porpoised three times and then came to a full stop. She taxied back to the departure end of the runway for a second takeoff. On her second landing the airplane porpoised four times, she taxied back to her flight school without further incident. As a result of the hard landing and subsequent porpoise, the flight instructor conducted a postaccident examination of the engine and airframe, and substantial damage to the firewall was discovered.
The student pilot reported there were no pre-impact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.