A possible arrowhead from Long Pond, Falmouth

Walking around Long Pond in Falmouth I was temporarily on the jogging path, looked down and spotted an interesting looking piece of quartz in the sand and gravel of the path. It sort of looked like an arrowhead but was pretty fresh looking, and it was hard to believe an arrowhead would be sitting out there in plain sight.
I looked around briefly for other signs of stone tools, saw a few other pieces of broken quartz, but decided that broken quartz in an active path is not surprising. I looked the piece over carefully not being sure any of the faceting was legitimate flaking, decided it was probably not anything, stuck it in my pocket, and continued my walk.
Then on my way back, I took a little longer to look around at the other gravel in the pathway at the spot where I picked this item up. That is when I spotted some flakes of black rhyolite ("felsite") with white inclusions. Around here, that is material that comes only from Quincy/Saugus or Westwood and it is not from glacial debris. So although it is possible to imagine a glacial cobble of quartz managing to get pulverized on an active footpath; it is harder to image this for an exotic lithic material that does not belong in Falmouth at all. This out of place rhyolite, together with the broken quartz and the possible "arrowhead" suggest a archeological site in the path.

I have convinced myself that I did indeed pick up an "arrowhead" and actually, since it is not aerodynamic, it would more likely be a small knife of some kind. There is a faint rust stain at the base where it would have been hafted.