PHYSICS LAB / MECHANICS

Projectile motion simulator

Ball 1

Launch settings

FLIGHT FIELD Ideal motion · No air resistanceTime: 0.00 s

Vertical position y–t

Speed v–t

Horizontal position x–t

Explore projectile motion

This free projectile motion simulator shows how a ball moves after an angled cannon launch. Change the initial speed, launch angle, height and gravity, then press Play. Select two balls to compare trajectories and use a start delay for the second launch. The x–t and y–t graphs show horizontal and vertical position; the speed–t graph shows the magnitude of velocity.

Motion equations and assumptions

With no air resistance and constant downward gravity, horizontal velocity stays constant while vertical velocity decreases with time. The launch angle θ is measured above the horizontal. Negative angles launch below the horizontal and are available when the initial height y₀ is greater than 1.00 m. For each ball, t is the time since its launch.

  • x(t) = v₀ cos(θ) t
  • y(t) = y₀ + v₀ sin(θ) t − ½gt²
  • vₓ = v₀ cos(θ), vᵧ(t) = v₀ sin(θ) − gt
  • Speed |v| = √(vₓ² + vᵧ²)

Flight time is the landing solution of y(t) = 0; range is the horizontal distance at landing. At equal launch and landing heights, a 45° launch gives the greatest range for a fixed initial speed. Raising the launch platform changes the flight time and the angle that gives the greatest range. Each animation ends at the ground; bounces and air drag are excluded.