(This is also typically why I don't do math......)
Just FYI, the speed of sound, fps of a 50cal rd, etc.. I went and looked up as I don't know them off the top of my head as some on here might. I've no military background so again, I don't mind the correction if one's forthcoming. :-)
If you were a tiny astronaut and could hop aboard the bullet at the muzzle, the g-forces of "slamming on the brakes" due to air resistance, would kill you in almost an instant. Ten or twelve g's causes pilots to black out. A hundred g's is about the greatest anyone has ever survived in a controlled environment, and that only briefly.
Anyhow, the brakes are on and the bullet is decelerating, in a major way, the moment the bullet leaves the muzzle.
By the time this particular 50-cal bullet reached its target 2.2 miles away, it was no longer traveling even at the speed of sound, and sound was catching up to it fast.
Now, all these reported numbers (10 seconds, 2.2 miles, etc.) are rounded off, and we don't know many other factors about this shot that ordinarily would come into play in doing ballistics calculations. So we can't say with any certainty whether the sound got there first or the bullet got there first, much less whether or not the dead jihadi heard the report before the bullet hit him, or before he died (different things), but my money's on him not hearing anything because of the back-of-the-envelope reasons I gave earlier.
It's your time of flight -- you assumed the bullet never slowed down.
Picking a military cartridge, the M33 ball, the time of flight to 3800 yards would be about 10.2 seconds. The velocity of the bullet at that range would be about 720 ft/sec.
Ballistic Calculator: http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi