Motion in three dimensions

Intermediate

Extend independent-axis analysis to x, y and z.

Treat x, y and z independently with constant-acceleration formulas, then combine as vectors. Speed is √(vx²+vy²+vz²).

Worked example

A drone at (3, 4, 12) m/s has speed 13 m/s.

Common mistake

Add one component at a time; don't take a sum of speeds.

In more detail

Three-dimensional motion uses x, y and z components for position, velocity and acceleration. The same ideas apply, with one extra component.

Drone navigation computes 3D position and velocity to follow a path.
Flight simulators model aircraft motion in three dimensions.
A drone flying up, forward and sideways must track x, y and z independently to hold a position in three-dimensional space.

Does gravity act in all three directions?

No. Gravity acts along one axis, usually vertically downward.

How do I find the speed in 3D?

Use the square root of the sum of the squares of the three components.

Do I need vectors for three-dimensional motion?

Yes. Use components along each axis, then combine them to find the magnitude of velocity or displacement.