Final answer:
The circus performer and the cannon ball follow a path known as projectile motion, which is a parabolic trajectory consisting of constant horizontal velocity and vertically accelerated motion due to gravity.
Step-by-step explanation:
The path that both the man and the cannon ball take when shot out of a cannon is a type of two-dimensional motion known as projectile motion. This path is characterized by a curved trajectory, which under the influence of gravity, is parabolic. When an object is projected into the air at an angle, it follows this path due to the constant acceleration downward from gravity, while maintaining a constant horizontal velocity (assuming no air resistance).
The projectile motion is composed of two components: the horizontal component, which is influenced by the initial velocity and remains constant if air resistance is ignored, and the vertical component, which is affected by gravity. The combination of these two motions results in the characteristic parabolic path. During such motion, the horizontal and vertical components of motion are independent of each other.