Tutorial · Projectile Motion

Simulate Projectile
Motion

Build a projectile experiment from scratch, verify the range formula, and see how air drag changes the landing point — all in your browser.

Contents
  1. The physics behind it
  2. Quickstart with the preset
  3. Build it from scratch
  4. Experiments to try
  5. Key formulas
Theory

The Physics Behind Projectile Motion

A projectile is any body in flight under the influence of gravity alone (or gravity + drag). The horizontal and vertical components of motion are independent of each other — this is the key insight that makes the maths tractable.

x(t) = v₀cos(θ)·t    y(t) = v₀sin(θ)·t − ½gt²Kinematic equations for a projectile launched at angle θ with speed v₀

The range (horizontal distance at landing) is maximised when θ = 45°. With no drag, the range formula is:

R = v₀² · sin(2θ) / gMaximum range at θ=45°: R = v₀²/g (BINAS: kinematica)
Real world The ideal parabola only holds in a vacuum. At high speeds, air drag dramatically shortens the range and shifts the optimal angle below 45°. PHYSIX models this with a configurable drag coefficient Cd.
Quickstart

Load the Built-in Preset

Open PHYSIX

Go to simverselab.com//physix/ and wait for the simulator to load.

Find the Presets panel

In the left panel, scroll down to the Projectiles group and click 🎯 Projectile 45°.

Press Play

Click the cyan ▶ PLAY button in the top bar. The projectile launches at 45° with v₀ = 30 m/s and a drag coefficient of Cd = 0.47.

Read the range

When the ball lands, use the 📏 Ruler tool (top bar) to measure the horizontal distance. Compare it to the formula: R = 30²/9.8 ≈ 91.8 m in vacuum.

From scratch

Build the Experiment Yourself

Clear the canvas

Click 🗑 CLEAR in the topbar to remove the solar system preset and start with a blank canvas.

Add a Ground Plane

Drag the ▬ Ground Plane tile from the Objects panel onto the canvas. It snaps to y = 0 by default.

Add a Sphere

Drag a 🔵 Sphere onto the canvas. In the right-hand Properties panel, set: mass = 0.5 kg, radius = 0.12 m, x = −35 m, y = 1.2 m.

Set initial velocity

In the Properties panel, set Vx = 21.2 m/s and Vy = 21.2 m/s. This gives v₀ = 30 m/s at exactly 45°.

Apply gravity

In the Forces panel (left panel, GRV tab), drag the Uniform g force tile onto your sphere. Leave gx = 0, gy = −9.80665 m/s².

Apply drag (optional)

From the FLD tab, drag Surface Drag onto the sphere. Set Cd = 0.47 (a sphere), autoA = true. This enables realistic air resistance.

Press Play & compare

Hit ▶ PLAY. Try toggling drag on/off (click the force chip in the right panel) and compare the landing positions.

Experiments

Things to Try

Angle sweep

Reset the simulation and try launch angles of 15°, 30°, 45°, 60°, and 75°. Plot range vs. angle. You should see a symmetric curve peaking at 45° — in vacuum. Does drag shift the peak?

Moon vs Earth

Change the gravity force to gy = −1.62 m/s² (Moon). Launch at 45° with the same speed. How much further does the ball travel? Does the formula still hold?

Heavy vs light ball

Duplicate the sphere (right-click → Duplicate). Change one to 0.01 kg and one to 100 kg. Launch both. With drag enabled, which lands first? Why?

Real baseball pitch

Set v₀ = 40 m/s (90 mph), Cd = 0.40, m = 0.145 kg (regulation ball). From x = 0, y = 1 m, what angle do you need to cross a 0.5 m high plate at x = 18.4 m?

Reference

Key Formulas

Vx = v₀·cos(θ)    Vy = v₀·sin(θ) − g·tVelocity components at time t
Range R = v₀²·sin(2θ) / gRange in vacuum. Angle for max range: θ = 45°
F_drag = ½·ρ·Cd·A·v²Aerodynamic drag. ρ = 1.225 kg/m³ at sea level (ISA)
Next tutorial Ready for more? Try the Pendulum & Chaos tutorial to explore simple harmonic motion and chaos theory in the same simulator.