Projectile Motion Physics

Key Equations

Time of flight: t = 2v₀sin(θ)/g. Maximum height: h = v₀²sin²(θ)/(2g). Horizontal range: R = v₀²sin(2θ)/g. At 45°, sin(2θ) = 1, giving maximum range. Air resistance is ignored in this model.

Optimal Launch Angle

Without air resistance, 45° gives maximum range for a level surface. With air resistance, the optimal angle is lower (typically 30–40°). For a projectile launched from a height, the optimal angle is below 45° — this calculator shows the adjustment.

Real-World Applications

Sports: ball trajectory in football, cricket, golf, basketball free throws. Engineering: artillery, water fountain design, irrigation. Physics experiments: validating equations of motion using projectile tracks.

Projectile Motion Calculator

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