Resolution of Vectors into Components
Any vector can be written as the sum of mutually perpendicular components, Ax = A cos t and Ay = A sin t.
What is Resolution of Vectors into Components?
Any vector can be written as the sum of mutually perpendicular components, Ax = A cos t and Ay = A sin t.
Key formula / rule: Ax = A cos t, Ay = A sin t with t measured from the x-axis.
Key points
- Resolve a vector along chosen perpendicular axes.
- Justify the choice of axes that minimises algebra in a given problem.
Common exam trap
Swapping sine and cosine when the angle is measured from the vertical.
Definitions
- Term
Resolution of Vectors into Components
- Meaning
Any vector can be written as the sum of mutually perpendicular components, Ax = A cos t and Ay = A sin t.
- Term
Resolution of Vectors into Components — explanation
- Meaning
Resolution turns a two-dimensional problem into two independent one-dimensional problems, which is the entire basis for treating projectile motion.
Learning objectives
Resolve a vector along chosen perpendicular axes.
Justify the choice of axes that minimises algebra in a given problem.
Formulae
- Key point
Ax = A cos t, Ay = A sin t with t measured from the x-axis.
- Key point
Perpendicular components are independent of each other.
- Key point
Choosing axes along the motion or along an incline reduces algebra.
Prerequisites
PHY-U1-KIN-T2-S1-C1
Common mistakes
Swapping sine and cosine when the angle is measured from the vertical.
Resolving along non-perpendicular directions and then using the Pythagorean form.
Keywords
Resolution
Vectors
Components
Practice preview
A vector has a magnitude of 10 units and makes an angle of 30 degrees with the positive x-axis. What are its x and y components?…
easy
A vector has an x-component of 3 units and a y-component of 4 units. What is the magnitude of this vector?…
easy
A displacement vector has components D_x = -5 m and D_y = 5 m. What is the angle this vector makes with the positive x-axis?…
medium