Determining the Optimal Launch Angle for a Volleyball Corner Serve Using Piecewise Quadratic Modeling and Video Analysis

This investigation seeks to determine the optimal launch angle for a volleyball corner serve to ensure it clears the net and lands in a specific target area.

Using primary data collected via video analysis and LoggerPro, the student models the ball's trajectory. The study compares a single quadratic model against a refined piecewise function to address inaccuracies in the flight path.

Statistical validation using Root Mean Square Error (RMSE) demonstrates the piecewise model's superior accuracy. The optimal angle is ultimately derived by applying calculus to find the initial gradient of the trajectory.

This exemplar is valuable for its sophisticated use of piecewise modeling, statistical error analysis, and the practical application of derivatives to real-world projectile motion.