Component Addition of
Vectors
Lesson 5
Announcements
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HW #4 due today
HW #5 due Tuesday
Optics HW #4 (Lab) due Wednesday
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Homework Quiz – Tuesday!!!
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Lunch Bunch – Optics lesson 5
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Lesson 5 – Component Addition of Vectors
AP Physics B Standard:

I. A. 2. a) Students should be able to add, subtract, and
resolve displacement and velocity vectors, so that they
can (1) Determine components of a vector along two
specified, mutually perpendicular axes.
Objectives:
• Students will be able to resolve vectors into horizontal and
vertical components.
• Students will be able to sum vectors using component
method.
Vector components
Practice Problem: Find the x- and y-components of the
following vectors
a)
b)
c)
R = 175 meters @ 95o
v = 25 m/s @ -78o
a = 2.23 m/s2 @ 150o
Practice Problem:
The x- and y- components of several vectors are given.
Calculate the magnitude and direction of the vectors.
a) Rx = 12 m, Ry = 3 m
b)
vx = 15 m/s, vy = -20 m/s
c)
ax = -25 m/s2, vy = -50 m/s2
Component Addition of Vectors
1) Resolve each vector into its x- and y-components.
2)
Ax = A cos
Bx = B cos
Cx = C cos
Ay = A sin
By = B sin
Cy = C sin
etc.
Add the x-components (Ax, Bx, etc.) together to
get Rx and the y-components (Ay, By, etc.) to get Ry.
3) Calculate the magnitude of the resultant with the
Pythagorean Theorem (R = Rx2 + Ry2).
4) Determine the angle with the equation  = tan-1
Ry/Rx.
B
By
A
Ay
Bx
R
Cy
C
Cx
Ax
By
Ay Cy
R
Ax
Bx
Cx
Practice problem: Vector A points in the +x direction and has a
magnitude of 80 m. Vector B has a magnitude of 30 m and has a
direction of 30o relative to the x axis. Vector C has a magnitude
of 50 m and points in a direction of -60o relative to the x axis.
Find the following graphically and by component.
a)
Find A + B
b) Find A + B + C
c)
Find B - C
a)
Component
Component
b)
Component
c)