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THE PHYSICS BEHIND THE GAME

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THE THREE BASIC SHOTS

In beer pong there is three basic shots: the arc-shot, the fastball, and the bounce shot. Each shot has its pros and cons and are generally used different situations during the game. For example, when a player intends to catch up or gain the lead by two cups the bounce shot is the best shot to use. Lets go over the basic physics in each shot.

THE ARC SHOT

This shot is characterized by maximizing the balls height resulting in a optimal angle of entry. In order to obtain this large maximum height there must be a large change in height from the release point to the peak height. This is achieved by maximizing the balls vertical velocity in the y-direction. The ball follows the path of a simple projectile motion. Due to the force of gravity the velocity in the y-direction accelerates negatively downward while the velocity in the x-direction remains constant. By using the simple kinematic equation below we can determine that the final velocity in the y-direction is proportional to the change in the height. Therefore an increase in the change in height corresponds directly to an increase in angle of entry thereby increasing the likelihood of making more cups.

THE FASTBALL

The fastball is characterized by its large horizontal velocity and small release angle. The fastball has a small change in height from release point to peak height resulting in a poor angle of entry. This shot is optimal in a situation of an outdoor game where players have a strong crosswind. With a shorter flight time the ball will be effective less intensely by external forces. This shot is also common when trying to knock your opponents cup over due to the balls large velocity in the x-direction.

THE BOUNCE SHOT

Last but not least we have the bounce shot. Similar to the fastball the bounce shot has a larger horizontal velocity than vertical velocity resulting in a lower angle of entry. However, if used properly the bounce shot can knock out two cups in one shot. During this shot there is topspin placed on the ball resulting in a change of air pressure between the upper and lower parts of the ball. There is a lower air pressure below the ball due to the fast moving air. The Magnus force drives the ball downward thereby increasing the y-velocity while decreasing the x-velocity. Once the ball collides with the table the concept of momentum comes into play. In this perfectly elastic collision, the small mass of the ball collides elastically with the large table, which is at rest. After the collision the ball still maintains its rotational motion and has similar velocity as it did prior to the collision. When the ball reaches its second peak the combination of forces due to gravity and the Magnus force results in the ball to accelerate in the downward direction. This acceleration creates a large change in the vertical direction corresponding to a greater angle of entry.