Unknown flight time in the boundary-value formulation of Mantle’s home run

Determine the total flight time of the baseball from launch at home plate (x=0, y=0.9 m) to impact at the Yankee Stadium facade (x=106.9 m, y=36 m) for Mickey Mantle’s May 22, 1963 home run, consistent with the ordinary differential equation model including gravity, quadratic aerodynamic drag, and the Magnus effect, given that the boundary-value problem provides final position but not the final time.

Background

The analysis treats Mantle’s home run as a boundary-value problem because some initial conditions (initial speed and launch angle) are unknown while the final position is known. In this setup, the flight time is not provided and must be inferred as part of the solution path.

This explicit lack of the final time prompts the need to either solve for it alongside the trajectory or to otherwise determine it consistent with the modeled forces (drag and Magnus effect).