VectorsVectorsVectorsVectors

What is a vector quantity?

Vectors

Vectors are quantities that possess magnitude and direction.

»Force»Velocity»Acceleration

What are scalar quantities?

Scalars• Scalars are quantities that possess

only magnitude.• How much money you have• How old you are• How tall you are• Temperature• Pounds• Speed• Length

Represent the following vectors

• A wind velocity of 20 mph due north• A boat traveling 4 knots per hour

heading east• A car traveling 60 mph heading south

Equal Vectors

• Same length• Same direction

Parallel Vectors

Adding VectorsAdding VectorsAdding VectorsAdding Vectors

Three Methods forAdding Vectors

• Tail to Head Method• Parallelogram Method• Component Method

Tail to Head Method

Adding Vectors Tail to Head

Draw Vector A with the correct length and angle.

Draw Vector B with the correct length and angle, but such the Vector B’s tail starts at the head of vector A.

The Vector C is then represented by an arrow from the tail of Vector A to the head of Vector B.

Adding Vectors Same direction

•

Adding VectorsOpposite directions

Adding Vectors

Components

Parallelogram Method

Parallelogram Method

Vector 1

Vector 2

Resulta

nt Vecto

r

Component Method

Component MethodFind the sum of Vector 1 and Vector

2.

Vector 1 is 25 m 50 N of E

Vector 2 is 10 m 45 N of W

Component Method• Using Trigonometry, find the x-

component and the y-component for each vector.

• Add up the x-components.• Add up the y-components.• Use the Pythagorean Theorem and the

trig functions to get the size and direction of the resultant vector.

Finding the x-component

cosadjacent

hypotenuse

X-component

Y-component

Resulta

nt vecto

r

Finding the x-component

Vector 1 is 25 m 50 N of E

X-component

Y-component

50

25 meters

cosadjacent

hypotenuse

ocos 5025 meters

x component

X-component = 25 * cos 50

X- component (vector 1) = 16.1 m

Finding the y-component

sinopposite

hypotenuse

X-component

Y-component

Resulta

nt vecto

r

Finding the y-component

Vector 1 is 25 m 50 N of E

X-component

Y-component

50

25 meters

y-component = 25 * sin 50

y- component (vector 1) = 19.2 m

osin 5025 meters

y component

Finding the x-component

Vector 2 is 10 m 45 N of W

X-component

Y-component

45

10 meterscos

adjacent

hypotenuse

ocos 4510 meters

x component

X-component = 10 * cos 135

X- component (vector 2) = -7.1 m

Finding the y-component

Vector 2 is 10 m 45 N of W

X-component

Y-component

45

10 meterssin

opposite

hypotenuse

osin 4510 meters

y component

y-component = 10 * sin 135

y- component (vector 2) = 7.1 m

Adding the x- components

Vector 1 + Vector 2

16.1 m+ -7.1 m = 9 m

Adding the y-components

Vector 1 + Vector 2

19.2 m+ 7.1 m = 26.3 m

Using the Pythagorean Theorem

c²= a²+ b²c²= 9²+26.3²c²= 772.69

c = 27.8 meters

tanopposite

adjacent

26.3tan

9

1 26.3tan

9

= 71.1 N of E

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Vectors on the GoVectors on the GoVectors on the GoVectors on the Go

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