According to the certified flight instructor (CFI), he was conducting a training flight with the student pilot on short field landings. During last short field landing, as the airplane flew over the runway numbers, the airplane dropped and landed hard. According to the student pilot, he recalled that the airplane was at 55 knots during short final. As the airplane began to descend, he attempted a go-around, but did not advance the throttle quickly enough and the airplane landed hard on the runway. During the examination of the airplane by a Federal Aviation Administration inspector, it was revealed that the firewall was buckled. The CFI and student pilot did not report any flight control malfunctions or failures that would have precluded normal operation.