General aviation pilot reported an NMAC while landing at a non-towered airport when another aircraft not communicating on CTAF took off opposite direction from the same runway.

Narrative

I was flying my RV-7 and landing on Runway XX at ZZZ. Before entering the pattern; I picked up the weather on the AWOS and the wind was listed as calm. The preferred calm-wind runway at ZZZ is XX.I made the standard radio calls in the pattern while flying downwind; base; and final to land on XX; and a Baron called while I was in the pattern also signaling a taxi to runway XX. While on short final; a Piper called that it was headed to runway YY. I made a radio call saying; 'Last caller; RV-7 short final XX.'While landing; I saw the Piper taking off on runway YY on a collision course. The Piper took off and made an evasive turn to his right. I added power and made an evasive turn to my right. We missed each other by around 100 feet at about 50 feet AGL. I went around and landed successfully.I made a radio call urging the Piper to use his radio and received no response. The FBO was able to confirm my radio was working when I requested a comms check during my go-around. It is not clear to me if the other aircraft's radio was receiving.