![]() Since the vertical motion is determined by the same acceleration that describes the motion of objects in free fall, a second cannon ball that is dropped at precisely the same instant as the first cannon ball is fired, will reach the ground at precisely the same instant. The combination of these two effects produces a path that describes a parabola. For example, if a cannon ball is fired in the horizontal direction, the velocity of the ball will remain constant in the horizontal direction but will accelerate toward the Earth in the vertical direction with an acceleration of 1 g. Therefore, a projectile in motion will remain with the same horizontal velocity throughout its flight, since no force exists in the horizontal direction, but its velocity will change in the vertical direction due to the force of gravity. As English physicist and mathematician Sir Isaac Newton (1642 –1727) proposed, an object in motion will remain in motion unless acted upon by an external force. Motion in the vertical direction where the force of gravity is present, and horizontal motion where the force of gravity is zero. The motion of projectiles without air resistance, can be separated into two components. 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. In addition, it is obvious that a rock will fall more quickly than a feather. It is well know that skydivers may change their altitude relative to other skydivers by simply changing the shape of their body. Air resistance, on the other hand, can vary greatly depending on altitude, wind, and the properties and velocity of the projectile itself. However, for most earthbound applications, the value of g can be considered constant (it only changes by 0.5% due to a 10 mi altitude change). The acceleration of gravity, g, becomes smaller as the distance from Earth increases. (Of course, a jet is not in free fall but is being accelerated by its engines and gravity.) By comparison, a pilot in a supersonic jet pulling out of a nose dive may experience an acceleration as high as 9 g (nine gee). ![]() This acceleration is equal to 1 g (commonly pronounced: one gee), where g stands for the acceleration due to the force of gravity (g). The change in speed per time interval is known as the acceleration and is constant. Thus, the change in speed for each one second time interval is always 32 ft per second. 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 (19.6 m) per second after two seconds, to a speed of 96 ft (29.4 m) per second after three seconds, and so on. It is also true that the speed of a falling object will increase by equal increments in equal periods of time. For the simplest case, when air resistance is negligible and when objects are close to the Earth ’s surface, Italian astronomer and physicist 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. In order to understand projectile motion it is first necessary to understand the motion of free-falling bodies -objects that are simply dropped from a certain height above Earth. Ballistics influences many fields of study ranging from analyzing a curve ball in baseball to developing missile guidance systems in the military. ![]() When air resistance is significant, however, the shape and rotation of the object are important and determining the flight path is more complicated. For objects projected close to Earth and with negligible air resistance, the flight path is a parabola. The path of the projectile is determined by its initial velocity (direction and speed) and the forces of gravity and air resistance. ![]() Such objects can include projectiles fired from cannons or small arms, bombs dropped from airplanes, or powered rockets. A projectile is an object that has been launched, shot, hurled, thrown, or by other means projected, and continues in motion due to its own inertia. Ballistics is the scientific study of the motion of bodies projected through space.
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