“Modelling the Optimal Shot Arc in Basketball: A Mathematical Analysis” Research Question: How does the angle of release and initial velocity affect the probability of a successful basketball shot from different distances?

This essay is for a IB math analysis and approaches standard level internal assesment

“Modelling the Optimal Shot Arc in Basketball: A Mathematical Analysis”

Research Question: How does the angle of release and initial velocity affect the probability of a successful basketball shot from different distances?

Relevant mathematical approaches

• Kinematics equation to model the projectile motion of the ball

• Calculate the optimal angle of release for different distances

• Determine the initial velocity needed for a successful shot at various angles

• Analyse how these factors contribute to the probability of scoring

• Use variables like initial velocity, angle of release, and the height of the basketball hoop

• Experiment on some stuff

• Talk about possible contribution of air resistance but in the IA it will be classified as negligible

Background:

Use the kinematic equations to model the path of the basketball as it travels from the my hand to the hoop

Use kinematics to calculate the vertical and horizontal motion of the ball