Falling Bodies, objects moving downward under the influence of gravity. The nature of this motion is the same for an object that falls straight down as it is for one that moves forward and down at the same time. Thus a bullet fired horizontally from a rifle falls at the same rate as one that is simply dropped. Knowledge of the motion of falling bodies is important in calculating the trajectory of bombs, bullets, artillery shells, and missiles.
In the fourth century B.C., Aristotle maintained that an object falls with a speed proportionate to its weightthat is, the heavier the object, the faster it falls. This idea was generally accepted until the 17th century, when Galileo showed that the rate of fall caused by gravity is the same for all objects. (There is a tradition that Galileo made this discovery by dropping iron balls of unequal weight from the Leaning Tower of Pisa. In describing his experiments, however, Galileo did not mention the Leaning Tower.) In an experiment made with balls rolling down a sloping board, Galileo determined the rate at which bodies accelerate (speed up) as they fall.
A seeming contradiction of the principle that all bodies fall at the same rate is the fact that a lump of lead will fall faster than such objects as feathers or leaves. However, these objects fall at a different rate because of air resistancein a vacuum, a lump of lead, a feather, and a leaf will fall at the same rate. This phenomenon was demonstrated by astronauts on the moon, which has no atmosphere. In one experiment, a hammer and a feather were dropped together from the same height; both fell at the same rate and struck the surface of the moon simultaneously.
In the mid-1980's, some physicists believed they had found evidence for a previously unknown force, much weaker than gravity, that would cause objects of different compositions to fall at very slightly different rates. Their report led to a number of experiments designed to detect such a force.
The law of falling bodies states:
A falling body in a vacuum accelerates at the rate of 32 feet, per second (9.8 m/s) during each second that it falls. This acceleration is called the acceleration of gravity, which is expressed mathematically as g. (In air, the body accelerates until it reaches its terminal velocitya constant velocity at which air resistance equals the force of gravity.)
The velocity (v) of a falling body that falls from rest is found by multiplying g by the time (t) during which a body falls: v = gt
For example, at the end of 5 seconds, a body will have a velocity of 32 X 5 = 160 feet per second.
The total distance (s) a body falls is equal to half of the acceleration of gravity multiplied by the square of the time: S=gt2/2
For example, at the end of the fifth second a body will have fallen
35 X 5 X 5/2=16X25 = 400 feet.