Vector Addition and Subtraction
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Transcript Vector Addition and Subtraction
Vector Addition
and
Subtraction
Do Now
Differentiate between a vector
and scalar
Give an example of each
Parallel Vectors
Add like numbers on a number line.
5
8
5 + 8 = 13
5
8
8-5=3
Perpendicular Vectors
Use Pythagorean’s Theorem to
determine the magnitude
Use Tangent to determine the
direction
Example
A person walks 40 m north and then 30
m east. What is their displacement?
b
a
a2 + b2 = c2
302 + 402 = c2
c = 50m
tan = opp/adj
= tan–1 (b/a)
Graphical Method
Assign a scale to the vectors
ex. 1N in problem = 1cm in diagram
Draw vectors head to tail using a
protractor to determine direction and
a ruler to determine magnitude.
Draw the resultant vector. Measure its
magnitude with a ruler and its
direction with a protractor
Parallelogram Rule
When two vectors have a tail at the
same place, they may be added
together by moving the tail of one
to the head of the other using a
parallelogram.
b
b
ad = ab + bd
d
a
a
c
c
Sample Problem
Solve Graphically and Algebraically
A plane flies with a velocity of 52 m/s
east through a 12 m/s cross wind
blowing the plane south. Find the
magnitude and direction (relative to due
east) of the resultant velocity at which it
travels.
An ambitious hiker walks 25 km west
and then 35 km south in a day. Find the
magnitude and direction (relative to due
west) of the hiker's resultant
displacement.
Adding Vectors that are not
Perpendicular
Select a coordinate system.
Draw and label vectors
Find the x and y components of all
vectors using trigonometric functions
SohCahToa
Use Pythagorean Theorem to find the
magnitude of the resultant vector.
Use trigonometric function to find the
angle of the resultant vector.