# Vector components

A vector has size and direction. You can split it into an x part and a y part using sine and cosine.

Physics (university) · Part 01: Motion and vectors · Card 6 of 8 · Last updated 2026-10-19

## Analogy

Like walking diagonally across a city: so many blocks east plus so many north.

## Example

**Splitting 50 N**

Fx = 50 cos 30 = 43.3 N
Fy = 50 sin 30 = 25.0 N

## In practice

A 50 N pull at 30 degrees above flat has a flat part of 43 N and an upward part of 25 N.

## Practice

### Flashcards

- **How do you find the x part of a vector at angle theta?** Multiply its size by cos theta.

### Interview questions

**A projectile is launched at 30 m/s at 40 degrees above flat ground. Explain how to find its time of flight and range.**

- Split velocity into components
- Vertical motion uses g to find time up and down
- Horizontal speed is constant, so range is that speed times time

## Questions people ask

### Why do we split vectors into components?

Perpendicular components do not affect each other, so you can solve each direction separately with simple algebra. A force at an angle becomes one sideways push and one upward push. After solving each, you combine them back if you need a final size and direction.

### How do I add two vectors that are at an angle?

Break each vector into x and y components. Add all the x parts together and all the y parts together. You then have the x and y components of the total. Use the Pythagorean theorem for the size and the inverse tangent for the direction.

## Related concepts

- [Projectile motion](https://studyvisually.com/learn/science/physics-university/physics-university-part-1/physics-university-part-1-concept-7)
- [Relative velocity](https://studyvisually.com/learn/science/physics-university/physics-university-part-1/physics-university-part-1-concept-8)

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