On May 10, 2004, approximately 1120 Pacific daylight time, a Cessna 172P, N54477, collided with the terrain during the landing roll at Goheen Field, Battle Ground, Washington. Neither the flight instructor or the dual student were injured, but the aircraft, which is owned and operated by Hillsboro Aviation, sustained substantial damage. The 14 CFR Part 91 instructional flight, which departed Hillsboro Airport, Hillsboro, Oregon, about 40 minutes earlier, was being operated in visual meteorological conditions. No flight plan had been filed. There was no report of an ELT activation. According to the instructor pilot, her student, who holds a private pilot certificate for helicopters, was working towards a fixed-wing add-on to his certificate. As per the lesson profile, the student planned a dual cross country flight to Toledo-Winlock, Washington (TDO), and then while en route, the instructor told the student to divert to Goheen Field. After arrival at the field, they over-flew the runway and determined that there was a direct crosswind at what they estimated was about 10 knots. The student then entered a left pattern for runway 15 for a full-stop landing on the damp turf runway. During his first two approaches, the student allowed the aircraft to get too high on final, and in both instances a go-around was initiated. According to both the instructor and the student, on the third approach the aircraft remained on the proper final approach path until it was approximately 50 feet above the ground. At that point the aircraft encountered a wind gust, and it ballooned upward to an extent that the student was not able to descend to a position where he felt comfortable initiating the landing flare until the aircraft was almost half way down the 2,600 foot runway. Then, according to the student, the aircraft "floated for awhile in ground effect" before touching down approximately two-thirds of the way down the runway. During this sequence of events, the student did not attempt to initiate a go-around on his own, and the instructor did not direct him to do one. After the aircraft touched down, the student applied the wheel brakes while holding the yoke full back for aerodynamic braking. Then, according to the student, the instructor came on the controls and assisted with the braking effort. Ultimately the pilots were unable to get the aircraft stopped before it went off the end of the runway, down a steep embankment, and into a ditch. Upon impacting the ditch, the nose wheel folded back and the aircraft sustained substantial damage. According to both the instructor pilot and the FAA Inspector that responded to the scene, there was no evidence of any problems with the aircraft's flight control or wheel braking systems.