The flight instructor reported that, during a simulated engine failure in the traffic pattern, with gusting wind conditions, the student pilot entered a forward slip on final approach. He added, that 10 to 20 ft. above the runway surface, "the wind gust we were riding suddenly halted wherein the aircraft began a rapid downward descent." The flight instructor reported that he "went for the flight controls to take command," but the student pilot at that same time applied back pressure on the flight controls. Subsequently, the airplane touched down hard, bounced back into the air, and the flight instructor performed a go-around. The flight instructor completed the subsequent traffic pattern and landing without further incident. The engine mounts and firewall sustained substantial damage. The flight instructor reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. An automated weather observation station at the accident airport, about the time of the accident, reported the wind from 170° at 16 knots, gusting to 24 knots. The flight instructor reported that the landing was on runway 15.