What is projectile motion?
It is the curved path an object follows when thrown or launched, pulled down by gravity while it keeps moving forward. The shape of that path is a parabola.
// physics › Time & Motion
Projectile motion
Range, peak height, and flight time of a projectile.
R = v² · sin(2θ) / g
Frequently asked questions
How is the range calculated?
Range is how far the projectile travels horizontally before landing: R = v² · sin(2θ) / g, where v is launch speed, θ the launch angle, and g gravity. The sin(2θ) term is why 45° gives the greatest distance.
Why does 45 degrees give the longest range?
Range depends on sin(2θ), which is largest when 2θ = 90°, i.e. θ = 45°. Steeper angles gain height but lose distance; shallower angles lose air time. 45° balances the two (ignoring air resistance).
Where is this used in real life?
Sport — the arc of a basketball shot, a long jump, or a golf drive. Engineering — water from a fountain or sprinkler, and the path of fireworks. Ballistics and safety — predicting where a launched object lands. Any time something is thrown and only gravity acts on it, this describes its flight.
What is flight time and peak height?
Flight time is how long it stays in the air, 2v·sin(θ)/g. Peak height is the highest point it reaches, v²·sin²(θ)/(2g) — both grow with a steeper launch angle.