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Projectile motion
Beginner
A launched body follows a parabola under gravity.
y = x tanθ − gx²/(2u²cos²θ)A projectile has constant horizontal velocity and constant downward acceleration g, so its path is a parabola. Split the initial velocity: ux = u cosθ, uy = u sinθ.
Launched at 20 m/s at 30°: ux = 17.3, uy = 10 m/s.
Acceleration is g everywhere, including the top, where only the vertical velocity is zero.
In more detail
Projectile motion is motion under gravity with an initial velocity. Horizontal velocity stays constant, while vertical velocity changes at g, giving a parabolic path.
Real-world uses
- Footballers' kicks and cricket throws follow projectile paths.
- Artillery and sports analytics use projectile models to predict landing points.
- Sports coaches use projectile motion to show why a long kick needs the right launch angle and speed, and video analysts measure the arc of a thrown ball.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What shape is the path of a projectile?
A parabola, if air resistance is ignored.
Does the horizontal velocity change?
No, not if air resistance is ignored, since there is no horizontal force.
Why is the path of a projectile a parabola?
The horizontal motion is uniform and the vertical is uniformly accelerated, so eliminating time gives y as a quadratic in x.
Related topics in Kinematics
Motion graphs from calculus · Terminal velocity · Two-dimensional motion · Time of flight · Maximum height · Horizontal range