Kingdom Basketball Association

🎯 Biomechanical & Physics Simulation Arena

A teaching sandbox — generic geometry and physics, drawn live on a hand-written canvas loop with zero framework overhead. No real athlete data is claimed anywhere on this page: the runner, defender and ball are teaching figures, and every number below comes only from the formulas printed here and the sliders you set.

The mathematics, printed in full

The target is a catch point D = 38 m downfield, with a catch window of ±2 m. With launch speed v, launch angle θ and gravity g — 9.81 m/s² by default:

• Range: R = v² · sin(2θ) / g
• Flight time: T = 2 · v · sin(θ) / g
• Range success: execution varies, modelled as a normal error with σ = 1.5 m — P_range = Φ((D + 2 − R)/σ) − Φ((D − 2 − R)/σ), where Φ is the standard normal cumulative distribution.
• Pursuit: the defender — a deep safety — starts L = 25 m from the catch point and runs at speed u, spread uniformly between 6.5 and 7.5 m/s, at pursuit angle φ off the direct line, so his effective closing speed is u · cos(φ) and his arrival time is T_d = L / (u · cos φ). He is late exactly when u < L / (T · cos φ), so P_late = clamp( (L / (T · cos φ) − 6.5) / (7.5 − 6.5), 0, 1 ).
• Success rate = P_range × P_late — the ball must both land in the window and arrive before the defender.

Change any slider and the rate recomputes from these formulas alone. The animation is illustrative; the rate is the formulas' output, not the animation's.