The Optimal Angle to shoot a Basketball


The choice to center the mathematical exploration around the topic of basketball was motivated by my love for the game. Therefore, I decided to explore the best angle and trajectory that can help players score during competitions. The study will supplement the existing research on calculus and contribute to its application in the real-life scenarios.

  1. Introduction

Basketball competitions are usually intense, and the best shooting technique is the key to the winning team. Therefore, since the game was invented in 1892 by Dr. James Naismith, all players have been aiming to shoot the basketball at the optimal angle (Bamberger 70). The game was first ignored in 1936 after the Berlin Olympic Games, but it now one of the most popular games with two national level competitions: America NBA and China CBA. Development in the current era has consistently been perfecting the basketball rules and improving the technique, which has made people all around to enjoy watching the game. Many types of research in techniques on basketball shooting have been done, for instance, Li Hui-Lin (2007) employed sports biomechanics analysis to study in the motion of shooting techniques of different hands, lower limbs, and waist as well as the relationships in shooting stability. On the contrary Zhou (2007) used the principles of sports mechanics to conduct research on the systematic and comprehensive analysis of shooting mechanical structure as well as rules of projection and shooting angles when shooting the ball in the air. He found out different shooting distances for projection and best incident angles.

When basketballers step up to shoot a ball, unless is they are mathematicians, they do not think about the shooting angle, effects air resistance on the trajectory of the shot, or where they need to aim regarding the rim, middle, front or back of the basket. A player like Shaquille O’Neal had a free throw percentage of 53.1 during the 2004 to 2005 season. His problem was that he shot about 45 percent from the foul line. Similarly, other NBA players have a similar problem and about a third of them shoot below 70 percent from the line (Bamberger 72). The paper presents models for basketball throws that use calculus to solve the shooting problems of players. The paper first agrees that some players have poor shooting because they through the ball at the wrong angle. Therefore, models will focus on the starting place, the release angle as well as the rules of basketball air movements.

  • Facts about the Best Free Shots

Various points determine a successful shooting of the player. They help interpret and refine mathematical models, and one of them is that the player learns the best way to shoot because consistency and height are important factors when it comes to controlling the release velocity and release angle. Therefore, if the player is taller, he or she should use a lower release angle to reach the rim. Taller players usually have an easier time when shooting free throws as compared to shorter ones because they are unlikely to make an error in release velocities and angles (Hamilton and Christoph 500). Regarding consistency, basketballers should consistently use the right release speed more than the right release angle. The other fact is that best shots do not pass through the hoop’s center, but between the back rim and the center (Hamilton and Christoph 500). So, shorter players should shoot towards the back rim while the taller one should aim the center…

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