# Ballistics

## Projectile Motion Without Air Resistance

The motion of projectiles without air resistance, can be separated into two components. Motion in the vertical direction where the force of gravity is present, and horizontal motion where the force of gravity is zero. As Isaac Newton (1642-1727) proposed, an object in motion will remain in motion unless acted upon by an external force. 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. For example, a cannon ball is fired in the horizontal direction. The velocity of the cannon ball will remain constant, in the horizontal direction, but the ball will accelerate toward the Earth, in the vertical direction, with an acceleration of 1 g. The combination of these two effects produces a path which describes a parabola. 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. Therefore, the motion in the horizontal direction does not affect the motion in the vertical direction. This fact can be confirmed by knocking one coin off the edge of the desk with a good horizontal whack, while a second coin is simultaneously knocked off the desk with a gentle nudge. Both coins will reach the ground at the same time.

By increasing the amount of gun powder behind the cannon ball, one could increase the horizontal velocity of the cannon ball as it leaves the cannon and cause the cannon ball to land at a greater distance. If it were possible to increase the horizontal velocity to very high values, there would come a point at which the cannon ball would continue in its path without ever touching the ground, similar to an orbiting satellite. To attain this orbiting situation close to the earth's surface, the cannon ball would have to be fired with a speed of 17,700 MPH (28,500 km/h)! In most instances, projectiles, like cannon balls, are fired at some upward angle to the earth's surface. As before, the flight paths are described by parabolas. (The maximum range is achieved by aiming the projectile at a 45° angle above the horizontal.) Angles equally greater or less than 45° will produce flight paths with the same range (for example 30° and 60°).