According to the flight instructor, he was demonstrating to a student pilot the technique required to land the airplane on a short runway over a 50-foot obstacle. About 50 feet over the runway, at an airspeed of 60 knots, with flaps fully deployed, the instructor reduced the throttle to idle and pitched the nose down to "increase airspeed" and flare the airplane before touchdown. Immediately after reducing the engine power to idle, the airplane "sunk," and the instructor responded with a full throttle application. However, the airplane was "too close to the ground," and the engine did not respond in time to prevent a hard landing, which resulted in substantial damage to the engine firewall. The instructor reported that there were no mechanical malfunctions or failures that would have precluded normal operation of the airplane.