It's winter time, so somebody is playing basketball SOMEWHERE just about everywhere in the country. Go sit 5-15 rows up from the floor such that you're somewhere between head level of the players and level with the basket, and pick a seat down at one end or the other, sooner or later someone is going to shoot a 3point shot.
You'll note that the ball goes ABOVE THE SHOOTER'S HEAD and that it also goes ABOVE THE RIM. Bullets do the exact same thing.
Bullets do not necessarily start dropping as soon as they leave the barrel, but rather they start experiencing downward acceleration (32ft/sec/sec). So we aim above the target such that the vertical component of the shot, so we put a vertical velocity component on our bullets (Vyo = muzzle vel * sin(angle above level)), knowing that the gravitational draw will begin counteracting it immediately after it leaves the barrel. Just like the basketball shot - we gotta throw the ball up above where we want it to hit on the backboard so gravity will bring it back to where we want it.
The physical formula for any shot, only considered by vertical displacement is this:
Y = Yo + Vyo*t + 1/2*a*t^2
Y is the elevation upon impact
Yo is the starting elevation
Vyo = the initial vertical velocity, i.e. the barrel is angled up slightly so it has some vertical velocity initially, again, this is calculated as muzzle vel * sin(angle of barrel)
a is the acceleration, in this case, a = G, acceleration due to gravity, -32.17ft/sec/sec
t in all cases is time, in this case, time of flight
So, if the target is level with the shooter, then Y = Yo, as the bullet will start and end at the same elevation. That leaves us with 0 = Vyo*t + 1/2*a*t^2, or Vyo*t = -1/2*a*t^2, divide by time on both sides, you get Vyo = -1/2*a*t
Substituting in G for a, since a, in this case, is the acceleration of Gravity, "G"
Vyo = -1/2*G*t There's your proof that we HAVE to shoot upward to hit our target, even if was perfectly level with the shooter.
For some real numbers:
6.8rem at 2650fps, with a BC of 400, at 600yrds, that comes out to 0.91sec Time of Flight (t).
Vyo = -1/2 * -32.17 ft/sec/sec * 0.91sec = 14.64ft/sec
So my vertical component needs to be 14.64ft/sec as it leaves the barrel to preempt the gravitational drop.
Just for fun, since the vertical component Vyo = muzzle vel * sin(angle of barrel), 14.64ft/s = 2650 * sin(angle). Sin-1(14.64/2650) = ~19MOA. Add 1.5MOA for a 1.5" sight height with a 100yrd zero, you get ~20.5MOA - my ballistic calculator shows ~21MOA total DROP (not drop below zero) at 600yrds for that particular round.
Another really simple way to learn something for yourself - take a rifle that you have zeroed at 100yrds, and get it on the page at 600. Dial the elevation. Now shoot at 100yrds on a VERY tall target, holding dead on zero. My 6.8SPC will hit about 18" high if I do this. Again, proof that bullets do have to be fired ABOVE the target and have to fly above the line of sight in order to drop back to target.