A projectile has horizontal range R and area A under its trajectory. Its launch speed is given by:
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A projectile has horizontal range R and area A under its trajectory. Its launch speed is given by:

G1 Physics · Accepted Answer

We know H = 3A/(2R). Also u² = g(R²+16H²)/(8H). Substitute H: 16H² = 16×9A²/(4R²) = 36A²/R², and 8H = 12A/R. Therefore u² = g[R²+36A²/R²] × R/(12A) = g[R³/(12A)+3A/R].