Skyhawk 172/Cutlass 172
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
IFR (cross country) [to] FVX. On final approach; we cancelled IFR; and switched over to the CTAF. I made radio calls stating that we were on a 10 miles; 5 miles; 2 miles; and short final for Runway 21. I told my student since it was a beautiful day; to be on the lookout for VFR traffic in the pattern; During the flare; my student and I noticed a homebuilt/experimental began a power off-180 from downwind straight to final for Runway 03 (the opposite end of the runway we were on). I made a radio call to let him know we were currently landing on 21. The aircraft dropped so much altitude in a short period of time that by the time we had touched down; the pilot (older male) was on short final. We taxied as quickly as possible off the runway but the other aircraft overshot final and looked like he was going to land in the grass alongside the runway -- which was where we were headed. We missed each other by 100 feet. (horizontal) I believe. We got out of the way; and he still side-stepped and landed on Runway 03. I made radio calls trying to reach him during the event to let him know we were on a possible collision path; but I got no answer. I believe he didn't have a radio.
C172 flight instructor reported on landing; an NMAC with opposite direction NORDO aircraft.