Here's the core idea of this entire lesson: any vector — no matter what angle it points — can be thought of as the result of adding two simpler vectors that are perpendicular to each other. One points purely horizontal, one points purely vertical. Together, they add up to the original vector.
The horizontal piece is called the x-component. The vertical piece is the y-component. Resolving a vector means finding those two component values.
Before resolving any vector, you choose a coordinate system — which direction is positive x, which is positive y. This choice is yours to make, and a smart choice can turn a hard problem into an easy one.
Once you've picked your axes, every vector in the problem gets resolved relative to that coordinate system — consistently, for the whole problem.
If you know a vector's magnitude and the angle it makes with the x-axis, three trig relationships let you find both components:
The first two break a vector into components. The third — the Pythagorean theorem — does the reverse: combines components back into the original magnitude. They're inverses of each other.
Adjust the magnitude and angle. Watch the vector resolve into its x and y components live.
A ball is kicked at 25 m/s at an angle of 30° above the ground. Find the horizontal and vertical components of its velocity.
Once a vector is resolved into components, something powerful happens: the horizontal motion and the vertical motion become completely independent. Whatever happens in the x-direction has zero effect on what happens in the y-direction, and vice versa.
This is why 2D motion in AP Physics 1 never actually requires new equations. You already know everything you need. The only new skill is realizing you have to do the same work twice — once per axis — and keep the two completely separate until the very end.
A projectile is anything launched into the air and left to move under gravity alone — a thrown ball, a launched rocket (before its engine cuts off), a kicked soccer ball. Projectile motion is the most common 2D motion problem in AP Physics 1, and it has a defining feature:
Zero acceleration. Velocity stays constant the entire flight. No force acts horizontally (ignoring air resistance).
Constant acceleration: g ≈ 10 m/s² downward. Velocity changes continuously — slows going up, speeds up coming down.
Launch a projectile. Drag the time slider and watch horizontal velocity stay constant while vertical velocity changes — two independent 1D problems, happening at once.
Notice: vₓ never changes as you drag the time slider. vy starts positive, hits zero at the peak, then goes negative.
A ball is launched at 30 m/s at 53° above the horizontal. Find the time it spends in the air and the horizontal distance it travels (use g = 10 m/s²).