For low angles of elevation used on level ground and short ranges, the vertical motion is approximately independent of the horizontal motion. This limits pointed bullets to 400 - 600 yards and blunt bullets to about 200 yards, near the limits for expansion and quick kills with these bullets. To put these equations to use, a value for K must be chosen. K has two functions. K accounts for the shape of the bullet and how air behaves when struck by a bullet.
Air is complex.
Its density and temperature and molecular speed distributions can vary. The drag on a bullet varies with the speed of the bullet varying with respect to the speeds of the molecules. On the other hand, one may well calculate with bullets of different shapes, so a factor representing properties of the bullet should be included. A number called the ballistic coefficient, C, is published for bullets from several manufacturers of bullets for reloaders. A long pointed bullet will have a much higher value of C than a short blunt bullet of the same material.