B737 FLT CREW HAS UNSTABILIZED APCH INTO PAFA.

Narrative

ON A VISUAL APCH TO RWY 1L AT THE FAIRBANKS ARPT WE BECAME HIGH ON OUR APCH PROFILE DUE TO STRONG TAILWINDS. THE APCH SEEMED NORMAL UNTIL APPROX 2000 FT AND 5 MI OUT WHEN WE REALIZED THAT THE TAILWIND WE HAD; WAS NOT DIMINISHING. (APPROX 35 KTS) THE RWY WIND WAS RPTED AS CALM. WE CONFIGURED TO FLAPS 40 DEGS AND SLOWED TO OUR FINAL SPD. THIS STILL DIDN'T LOOK LIKE IT WOULD BE QUITE ENOUGH CORRECTION; SO WE REQUESTED S-TURNS ON FINAL FROM THE TWR CTLR. THIS WAS APPROVED. WE MADE 2 TURNS L AND 1 TURN R BUT; DIDN'T GET FULLY STABLE UNTIL APPROX 300 FT AGL. AT ONE POINT THE GND PROX WARNING DID GIVE US A SINK RATE AND A PULL UP WARNING WHICH WE COMPLIED WITH. THE TOUCHDOWN WAS MADE SMOOTHLY IN THE TOUCHDOWN ZONE AND THE ROLLOUT WAS NORMAL (TXWY M). THE ACFT WAS ALWAYS UNDER COMPLETE CTL; AND I DON'T FEEL THAT SAFETY WAS COMPROMISED IN ANY WAY. THE ONLY PROB I SEE IS THAT WE DID NOT MEET THE STANDARD FOR A STABILIZED APCH. GOING AROUND AND RE-ENTERING THE PATTERN MAY HAVE BEEN A BETTER OPTION.