Ping Pong Ball Trajectory: Parabolic or Not?

Introduction
When a ping pong ball is hit or thrown, it follows a particular trajectory determined by various factors such as initial velocity, angle, air resistance, and gravity. The shape of this trajectory has been a subject of interest, and it is often debated whether a ping pong ball follows a parabolic path or not.

Parabolic Trajectory
A parabola is a symmetrical curve defined by a quadratic equation. It is characterized by its vertex, which represents the highest or lowest point on the curve, and its axis of symmetry. In a perfect, idealized scenario with no external forces, a projectile's trajectory would indeed follow a parabolic path due to the influence of gravity.

Factors Affecting Ping Pong Ball Trajectory
1. Initial Velocity: The speed at which a ping pong ball is hit or thrown affects its trajectory. Higher initial velocities result in longer and flatter trajectories, whereas lower velocities lead to shorter and steeper paths.

2. Angle of Projection: The angle at which the ball is launched also impacts its trajectory. Different launch angles can result in various curved paths, including parabolic, elliptical, or even linear in certain cases.

3. Air Resistance: Unlike the idealized scenario, real-world conditions involve air resistance, which affects the trajectory of a ping pong ball. Air resistance tends to slow down the ball and alter its path, causing deviations from a perfect parabolic trajectory.

Ping Pong Ball Trajectory in Reality
Due to the combined influence of gravity and air resistance, the trajectory of a ping pong ball in reality deviates from a perfect parabolic shape. The extent of this deviation depends on the initial velocity, angle of projection, and the density and speed of the surrounding air.

In practice, a ping pong ball's trajectory can be best described as a combination of a parabolic arc and other factors such as drag, lift, and spin. These additional forces introduce complexities that result in variations from a pure parabolic path.

Conclusion
While a ping pong ball's trajectory is influenced by factors such as initial velocity, angle of projection, air resistance, and gravity, it is important to acknowledge that it does not strictly adhere to a parabolic path. The presence of air resistance and other forces causes the trajectory to deviate from a perfect parabola, resulting in a more complex and dynamic path.

Why??