The flight instructor said that during a landing, the student pilot flared too high, and he took control of the airplane. The airplane landed hard, and the tail tie down hook was displaced into the fuselage. Although the instructor conducted a post flight inspection of the airplane, the damage was not discovered. The flight instructor performed the next takeoff, and he noticed that the elevator flight control was sluggish and minimally responsive. Additionally, the climb performance was poor. He landed the airplane without further incident. Another inspection of the airplane was performed, and the damage was discovered.