The Monkey and the Gun

 When hunting the wiley Stuphedwithstuph Monkey the hunter is always faced with a problem.  The Stuphedwithstuph Monkeys have developed a sixth sense that allows them to let go of their branch the instant that a bullet leaves the muzzle of a gun.  The age old question among hunters has been "Where should a hunter aim to actually hit the Stuphedwithstuph monkey? A) Above the monkey. B) Directly at the monkey. C) Below the monkey. The hunters have always believed that they should aim beneath the monkey so that the monkey will drop right into the path of the bullet.  Individual hunters all disagree when it comes to how far below the monkey they should aim.  Since no one has ever successfully shot a Stuphedwithstuph monkey the question has remained unanswered.   Where should you aim?
Myth
Bullets fly so fast that they are unaffected by gravity.
Fact
A bullet is a projectile and as such, its horizontal motion is unrelated to its vertical motion.  Just because it is moving rapidly in the horizontal direction does not mean that it will fall any slower than an object that is not moving horizontally. They still fall with the acceleration due to gravity ().
 If there was no gravity, the bullet would follow the blue line and the monkey would stay at the horizontal red line Since both the monkey and the bullet are accelerating due to gravity, they are both falling at the same rate. This means that at any given point in time after the bullet is fired and the monkey lets go, the displacement of  the bullet  from the blue line and the displacement of the monkey from the red line are equal. The vertical displacements continue to be equal to each other until ether the monkey or the bullet hits the ground.   If the blue line crossed the original position of the monkey (i.e. the gun was aimed directly at the monkey) then the bullet and the monkey will eventually be forced (quite painfully) to occupy the same space at the same time.  If the gun were aimed above the monkey, then the bullet would pass right over the monkey as they fell. If the gun were aimed beneath the monkey, then the bullet would pass beneath the monkey as they fell. Obtain Quicktime 3.0 from APPLE See for yourself by watching this simulation of a Stuphedwithstuph monkey encountering a gun aimed directly at the monkey.

Sights on guns are used to adjust for the effects of gravity on a bullet.   When you set the sights on a gun, you must set them for the range you are likely to be shooting from.  Basically what you are doing is adjusting the "Line from sights" to cross the "Bullet path" at the distance you will likely be shooting from.  Beyond this length, your bullet will hit low, closer than this length, your bullet  will hit high.  This also only sets your gun correctly for level ground.  If you shoot down from a hill, your bullet will hit high or if you shoot up a hill (dangerous practice) your bullet will hit low.