Mechanics, Planetary Motion and the Modern Science Revolution 61
direction, which was originally zero, will begin to increase once it is
driven off the top of the cliff because of the pull of the Earth’s
gravitational field. Its motion in the vertical direction is unaffected by its
horizontal velocity and it falls to the ground at the same rate as a car just
pushed over the edge. The two cars would take the same time to hit the
ground. However, the car originally traveling 30 m/s will have fallen the
distance from the foot of the cliff that a car traveling at 30 m/s would
have traveled on the ground from the foot of the cliff in the time it takes
the car driving off the cliff to fall to the ground. Fig. 6.4 shows three
cars, the one driven off the cliff at 30 m/s, the one, which just falls over
the edge and an imaginary car traveling at 30 m/s on an imaginary road
extended over the edge of the cliff. The time when each of the three cars
reaches their respective positions is represented by their distance from
the y-axis. Fig. 6.4 illustrates how the path of the car driven of the cliff at
30 m/s is a superposition of the paths of the two cars.
Fig. 6.4Galileo formulated the principle of superposition in the following
manner: If a body is subjected to two separate influences, each producing
a characteristic type of motion, it responds to each without modifying its
response to the other. This means if two or three forces act on a body the
net effect of these forces is simply their sum. This is illustrated by
considering the car sitting on top of the cliff. The force of gravity is
pulling it down but the ground upon which it sits is also pushing up on
the car with an equal and opposite force so the car does not fall, since the