Component Method

A vector can be broken into its components , which

are a vector parallel to the x-axis and another

parallel to the y-axis. This can always be done and

the following vector equation is true.

A = Ax + Ay

The process of breaking a vector into its component

is sometimes called VECTOR RESOLUTION.

• Vectors can be decomposed into components

• A vector in 2D can be thought of as having 2 parts

How can we use the component method in getting value of the Resultant Vector?

+ y

+ x

- x

- y

Sin Ө = opp/hyp

Cos Ө = adj/hyp

Tan Ө = opp/adj

= Ry / R

= Rx / R

= Ry / Rx

Break down each vector into its x- and y- components using the following formula;

Ax = A cos Ө Ay = A sin Ө

Where Ө is the angle measured counterclockwise

from +x axis

Add or subtract all the x- components together.

Add the y- components together.

Σx = _______ Σy = _______

Use Pythagorean Theorem to find the

magnitude of VR.

R = Rx2+Ry

2

To find the angle of the resultant vector use :

Ө = tan -1 Ry

Rx

A

B

R Ay

Ax

By

Bx

Ay

Ax

By

Bx

Ay

Ax

By

Bx

Ay

Ax

By

Bx

R A

B

Vector A has a length of 14 cm at 60o with

respect to the x axis, and vector B has a

length of 20cm at 20o with respect to the

x axis. Using the component method,

determine the resultant vector.

A man exerts a force of 60 N along the

handle of a lawn mower to push it across

the lawn. If the handle is held at an angle

of 30o with the lawn, what are the

horizontal and vertical components of the

force exerted by the man?

HERE COMES THE MATH

• Trigonometry

• Decompose vectors into

their components

• Horizontal: x

• Vertical: y

A

B By

Bx

Ay = A sin θ

Ax = A cos θ

θ

Decompose the following set of vectors:

1. 30 m/s 60 N of E

2. 15 m/s 30 W of N

3. 60 m/s S

4. 20 m/s SE

5. 40 m/s 30 S of E

6. 50 m/s 60 W of S

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