Projectile Motion Simulator (Physics)
Explore classic kinematics by launching a projectile at a chosen speed and angle. This simulator plots the trajectory, animates the motion, and reports time of flight, max height, range, and impact velocity. Everything runs in your browser.
Inputs
Educational physics model. Air resistance uses a simple linear drag approximation.
Results
Time of flight
2.884 s
Range
40.789 m
Max height
10.197 m
Impact speed
20 m/s
Gravity used: 9.807 m/s² • Launch speed (m/s): 20
Projectile motion snapshot
Projectile Motion Simulator
Speed: 20 m/s • Angle: 45° • Height: 0 m • Drag: off
Time
0 s
Position
x=0 m
y=0 m
Velocity
vx=14.14 m/s
vy=14.14 m/s
Assumptions: flat ground, constant gravity. No-drag uses closed-form kinematics; drag uses a simple linear model for teaching intuition.
Projectile motion equations (no air resistance)
In the simplest model, gravity is constant and the only acceleration is downward: \(a_x = 0\) and \(a_y = -g\). If the initial speed is \(v_0\) and the launch angle is \(\theta\), the horizontal and vertical components are \(v_{x0} = v_0\cos(\theta)\) and \(v_{y0} = v_0\sin(\theta)\). The position over time is:
x(t) = vₓ₀·t
y(t) = h₀ + vᵧ₀·t − ½·g·t²
Time of flight, max height, and range
Time of flight is found by solving \(y(t)=0\) for the positive root. Max height occurs when vertical velocity crosses zero. Range is the horizontal distance at impact. This tool computes those values and shows how they change with angle, speed, gravity, and launch height.
Air resistance (simple model)
Air resistance depends on many factors and is often modeled with quadratic drag in advanced physics. For teaching intuition, this simulator offers a simple linear drag toggle that adds a force proportional to velocity. Enabling drag reduces range and max height, and changes the impact speed.
Notes and privacy
This tool is educational and makes simplifying assumptions (flat ground, constant gravity, stylized drag model). It runs entirely in the browser and stores your last settings in localStorage for convenience (clearing site data removes that history).