Vector components
A vector has size and direction. You can split it into an x part and a y part using sine and cosine.
Last updated
Analogy
Like walking diagonally across a city: so many blocks east plus so many north.
Example
Fx = 50 cos 30 = 43.3 NFy = 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.