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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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