Physics · Lesson 17

3D Kinematics Laboratory

Most students think 3D motion is one giant scary equation. It is not. It is three smaller 1D stories running at the same time: one for X, one for Y, and one for Z. Fly the drone, isolate a single axis, and watch the others stay honest.

Dimension Collapse Fix

Three.js Flight Lab Live Telemetry Vector Decomposition Trail History

Mission Prompt

Try this first: hold Space for altitude, then let go and add W or D. Notice how your upward velocity history changes independently from your horizontal drift.

Flight HUD

Altitude (Z) 0.0 m

Speed Magnitude 0.0 m/s

Acceleration Magnitude 0.0 m/s²

X Position 0.0

Y Position 0.0

Heading 0°

W A S D Move on the floor plane

Space Shift Raise or lower altitude

Concept Check: fire the drone straight up with the blue Z vector, then add horizontal thrust. The altitude graph keeps telling the Z-story while the floor drift only rewrites the X and Y stories. That is vector independence in plain sight.

Mission Control

Read The Three Stories

The drone never solves “3D motion” all at once. It updates position, velocity, and acceleration component-by-component every frame.

X Axis s=0.0 · v=0.0 · a=0.0

Y Axis s=0.0 · v=0.0 · a=0.0

Z Axis s=0.0 · v=0.0 · a=0.0

Position History s(t)

Velocity History v(t)

Acceleration History a(t)

SuperpositionEach axis can be solved as its own 1D problem, then recombined into one 3D state vector.
Laser LogicThe red, green, and blue arrows show how total velocity is built by adding independent components.
Trail MemoryThe ribbon traces the drone’s history in space, which makes changes in direction easier to read than raw numbers alone.

Why It Matters

Robotics, Drones, and Orbital Motion

Every autonomous system treats 3D motion as decomposed axis math. Drone stabilizers, robotic arms, spacecraft guidance, and camera rigs all forecast X, Y, and Z independently before recombining them into one next move.

Mental Model

Three Sliders, Not One Mystery

If thrust only changes one component, only that component’s graph bends. That is the core mental shift this lesson is trying to build: 3D motion is not more magical than 1D motion, just more layered.

Teacher Move

Quick Demo Prompt

Ask students to predict what happens if you hold Space and then tap A. Have them name which graph should change first and which axis should stay untouched.

Practice

Concept Checks

Easy1. If the drone rises straight up and does not drift sideways, which velocity component is nonzero?

Hint: straight up changes only altitude, so only the vertical component is active.

Easy2. If you add thrust in X, what happens immediately to the Z velocity component?

Hint: axis independence means one component does not change because another one does.

Medium3. A drone has velocity components vx = 3 m/s, vy = 4 m/s, vz = 0 m/s. What is the total speed magnitude?

Hint: use the Pythagorean theorem on the component vector: √(3² + 4² + 0²).

Challenge4. The drone starts from rest. After one second, only vz has increased to 2 m/s while vx and vy stay zero. What axis had acceleration?

Hint: acceleration changes velocity, so whichever velocity component changed had acceleration.