PhysSandbox

Projectile Motion Simulator

This lab models ideal projectile motion in a uniform gravitational field: a point mass launched with speed and angle, with optional air resistance off by default. Trajectories, velocity components, and range follow from constant downward acceleration.

Who it's for: High-school and intro college physics; anyone learning kinematics in 2D and vector decomposition.

Key terms

  • projectile motion
  • parabolic trajectory
  • range
  • time of flight
  • kinematics
  • launch angle

Live graphs

How it works

A projectile is any object thrown into the air with an initial velocity, subject only to gravity (and optionally air resistance). The path followed is called a trajectory, which is parabolic in shape when air resistance is negligible. The range, maximum height, and time of flight all depend on the launch angle, initial speed, and gravitational acceleration.

Key equations

Position:x = v₀·cos(θ)·t,   y = v₀·sin(θ)·t − ½gt²
Range:R = v₀²·sin(2θ) / g
Max Height:H = v₀²·sin²(θ) / (2g)

Frequently asked questions

Why is the path a parabola?
With constant gravity and no drag, horizontal motion is uniform while vertical motion has constant acceleration. Eliminating time gives y as a quadratic function of x — a parabola.
Does mass affect the trajectory?
In this ideal model without air resistance, mass cancels out of the equations of motion; all bodies follow the same path for the same initial velocity and gravity.
What do the graphs show?
Typical views plot position and velocity versus time so you can tie the motion on screen to x(t), y(t), vₓ, and vᵧ and compare with textbook formulas.

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