The student pilot was on the second leg of a solo cross county training flight. During the flare at the destination airport, he landed the airplane "hard" and it bounced twice before he was able to regained control. He taxied back to the beginning of the runway and conducted a run-up. Noting no anomalies, he taxied onto the runway and started the takeoff roll. During the takeoff, he pulled back on the yoke "too far" and the airplane climbed between 30 and 40 feet before entering an aerodynamic stall and colliding with the ground. The nose gear collapsed and the propeller struck the ground, resulting in substantial damage to the fuselage. The pilot reported that there were no mechanical anomalies with the airplane before the landing. It could not be determined whether the airplane incurred damage during the hard landing that would have impacted the pilot's ability to maintain pitch control during takeoff.