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VECTORS. Recall that a vector has both:. Direction. Magnitude. The sum of two vectors is considered the resultant vector. +. Vector A. Vector B. A + B = R. Graphical Method. You must add vectors from head. head. to tail. tail. so. +. Vector B. Vector A. equals. Vector R.

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Presentation Transcript
slide1

VECTORS

Recall that a vector has both:

  • Direction
  • Magnitude
slide3

Graphical Method

You must add vectors from head...

head

to tail...

tail

so...

slide4

+

Vector B

Vector A

equals

Vector R

slide5

For Example:

A man walks 275m due east then another 125 m due east. What is his resultant displacement?

slide6

A man walks 275m due east then another 125 m due east. What is his resultant displacement?

PART 1

PART 2

275 m

125 m

Using a ruler you measure from the beginning of part 1 to the end of part 2

slide7

RULER

A man walks 275m due east then another 125 m due east, what is his resultant displacement?

PART 1

PART 2

275m

125m

slide8

RULER

A man walks 275m due east then another 125 m due east. What is his resultant displacement?

275m

125m

slide9

RULER

=

RESULTANT

400m

275m

125m

slide12

A man walks 275m due east then another 125 m due west. What is his resultant displacement?

PART 1

275 m

slide13

A man walks 275m due east then another 125 m due west. What is his resultant displacement?

PART 2

125 m

Using a ruler, measure from the beginning of part 1 to the end of part 2

slide14

RULER

A man walks 275m due east then another 125 m due west. What is his resultant displacement?

slide15

RULER

A man walks 275m due east then another 125 m due west. What is his resultant displacement?

275m

125m

slide16

RULER

=

RESULTANT

150m

275m

125m

slide19

A man walks 275m due east then another 125 m due north. What is his resultant displacement?

N

PART 2

125 m

PART 1

E

275 m

slide20

Using a ruler you measure from the beginning of part 1 to the end of part 2

125 m

PART 2

PART 1

275 m

E

N

slide23

302m

=

N

RESULTANT

E

slide24

Now we have the magnitude of the resultant vector we need a direction for the resultant vector

so…

We get our protractors out and measure the angle of the resultant vector

slide25

302m

=

N

RESULTANT

24.4°

E

slide26

Resultant Vector

302 m; 24.4° North of East

slide27

ANGLE NOTATION

On the last one we wrote 40° “North of East”, b/c we were saying it went 40° North “from” East.

In your notebook try the following for practice

slide28

N

W

E

S

30°

slide30

N

W

E

S

30°

slide32

N

W

E

S

30°

slide34

N

W

E

S

30°

slide36

N

W

E

S

30°

slide38

N

W

E

S

30°

slide40

N

W

E

S

30°

what direction is a vector directed northeast or southwest1
What direction is a vector directed “northeast” or “southwest”?
  • By definition, “northeast”, “southeast”, “southwest”, and “northwest” are vectors directed at 45 degrees.
slide45

When vectors are added at right angles to each other, the Pythagorean Theorem can be used to determine the magnitude of the resultant.

Trigonometric functions can be used to determine the direction.

slide46

A plane travels at 450 km/h due north with a wind blowing at 120 km/h due east. What is the resultant velocity of the plane?

120 km/h

450 km/h

slide47

120 km/h

450 km/h

tan = 120/450

R = 466 km/h 15 east of north

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