Projectile Motion Calculator
Projectile motion describes the parabolic path of an object launched into the air and subject only to gravity (ignoring air resistance). Key equations relate launch speed, angle, maximum height, horizontal range, and time of flight.
- 1Horizontal: x = v₀ × cos(θ) × t (constant velocity)
- 2Vertical: y = v₀ × sin(θ) × t − ½ × g × t²
- 3Max height: H = (v₀ × sin(θ))² / (2g)
- 4Range (flat ground): R = v₀² × sin(2θ) / g · max at θ=45°
Launch 20 m/s at 30°=Range: 35.3m · Max height: 5.1m · Flight time: 2.04s20²×sin60°/9.81=35.3m
Air resistance
Real projectiles experience drag. A golf ball without dimples would travel ~50% the distance of a dimpled ball — aerodynamics dramatically affect range at high speeds.
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Fun Fact
Galileo Galilei first described projectile motion as parabolic around 1608, disproving Aristotle's claim that objects naturally follow straight lines. He used inclined planes and balls to derive the equations without calculus.
References
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