Vector components
- Intro Lesson6:06
- Lesson: 16:15
- Lesson: 29:05
- Lesson: 317:30
Vector components
Lessons
In this lesson, we will learn:
- What are x and y components?
- How to break a vector into its components
- Problem solving with vector components
Notes:
-
Components of a vector are other vectors that add up tip-to-tail give you the original vector.
- The x and y components of a vector are the components that are pointed directly in the x and y directions, respectively, and are useful for solving problems.
- The x and y components can be found with trigonometry, since they always form a right triangle with the original vector.
sin(θ)=hyp.opp.
cos(θ)=hyp.adj.
tan(θ)=adj.opp.
a2+b2=c2 (Pythagorean theorem)
θ: angle, in degrees (°)
opp.: side opposite angle
adj.: side adjacent angle
hyp.: hypotenuse of triangle (longest side, side opposite 90° angle)
a and b: non-hypotenuse sides of triangle
c: hypotenuse of triangle
- IntroductionIntroduction to vector components:
- What are x and y components?
- How to break a vector into its components
- 1.Break a displacement into vector components
A boat sails 33.0 km at 55.0° north of west. What are the north and west components of its displacement?
- 2.Use components of velocity for calculations
A plane that is taking off travels at 67.0 m/s at a 15.0° angle above the horizontal.
i. How long does it take the plane to reach its cruising altitude of 12.0 km?
If the plane is headed east, how far east has it travelled in this time?
- 3.Add two 2D vectors using components
Solve the equation v1+v2=vres by breaking v1 and v2 into their x and y components.