Vector Components

Any vector can be split into two perpendicular components, one along x and one along y. Together they make the original vector, tip to tail.

Fx drags the sled forward, Fy lifts it; together they rebuild F.

With θ measured from the x axis, the components are the sides of a right triangle:

Fx = F cos θ, Fy = F sin θ

A rope pulls a sled with 40 N at 30° above the ground. The part that drags the sled forward is Fx = 40 cos 30° ≈ 34.6 N, and the part that lifts it is Fy = 40 sin 30° = 20 N.

Components make vectors easy to add: add all the x parts, then all the y parts.

On the board. The Components step does this with arrows, in two parts. First mark the angle: pick the axis θ is measured from and type θ. Then drag the two parts from the dot: F cos θ along that axis, F sin θ along the other one.