According to the flight instructor, he was demonstrating the technique required to land the airplane over a 50-foot obstacle to a short runway. At 50 feet over the runway, 60 knots airspeed, with flaps deployed, he reduced the throttle to idle and pitched the nose down to "increase airspeed" and flare the airplane prior to touchdown. Immediately after reducing the engine power to idle, the airplane "sunk" and the instructor responded with a full-throttle application. 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.