The flight instructor and student departed on an instructional flight and flew to a nearby grass airstrip for pattern work. Although the flight instructor had flown into the airstrip before, he did not check the runway length before the flight departed and thought it was longer than the actual published 2,400-ft length. After arriving at the destination airstrip, the student entered left downwind for runway 13, resulting in a right quartering tailwind of about 5 knots. The flight instructor told the student to perform a short field landing. The student turned early onto the base leg of the airport traffic pattern, then turned onto final approach, resulting in the airplane being high and fast. After informing the student that the airplane was high and fast, the student pitched the airplane down, which increased the airspeed, but he did not reduce power. The airplane continued to be high and fast, and somewhere before the midpoint of the runway the flight instructor told the student to go around. He repeated the instruction after the student hesitated. The student leveled off, added full power, removed carburetor heat, but left the flaps extended at 30° while he pitched for Vx airspeed. While climbing slightly, and with insufficient runway remaining to land, the flight instructor took the controls from the student and at that time realized the flaps were still at 30°. The airplane subsequently collided with trees beyond the end of the runway before descending to the ground resulting in substantial damage to the fuselage, wings, and empennage. The flight instructor reported there was no preimpact mechanical failures or malfunctions of the airplane that would have precluded normal operation. He also reported that the accident could have been prevented by executing a go-around much earlier.