In order to understand projectile motion it is first necessary to understand the motion of free-falling bod ies—objects that are simply dropped from a certain height above Earth. For the simplest case, when air resistance is negligible and when objects are close to the earth's surface, Galileo Galilei (1564-1642) was able to show that two objects fall the same distance in the same amount of time, regardless of their weights. It is also true that the speed of a falling object will increase by equal increments in equal time periods. For example, a ball dropped from the top of a building will start from rest and increase to a speed of 32 ft (9.8 m) per second after one second, to a speed of 64 ft (19.5 m) per second after two seconds, to a speed of 96 ft (29.4 m) per second after three seconds, and so on. Thus, the change in speed for each one second time interval is always 32 ft per second. The change in speed per time interval is known as the acceleration and is constant. This acceleration is equal to 1 g, which stands for the acceleration due to the force of gravity. By comparison, a pilot in a supersonic jet pulling out of a nose dive may experience an acceleration as high as 9 g (of course, a jet is not in free fall but is being accelerated by its engines and gravity).
The acceleration of gravity, g, becomes smaller as the distance from Earth increases. However, for most earthbound applications, the value of g can be considered constant (it only changes by 0.5% due to a 10 mi [16 km] altitude change). Air resistance, on the other hand, can vary greatly depending on altitude, wind, and the properties and velocity of the projectile itself. It is well know that sky divers may change their altitude relative to other sky divers by simply changing the shape of their body. Also, it is obvious that a rock will fall more quickly than a feather. Therefore, when treating problems in ballistics, it is necessary to separate the effects due to gravity, which are fairly simple, and the effects due to air resistance, which are more complicated.