vectors notes

8/2/2019 Vectors Notes

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Unit Two: VECTORS

Saline High PhysicsMr. Frederick


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Motivating Question: An Airplane fliesnorth with an airspeed of 575 mph. Ifthe wind is blowing 30 north of eastat 50 mph, what is the speed of the

plane as measured from the ground?What if the wind blew south of west?


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Vectors vs. Scalars

One of the numbers below does not fit in thegroup. Can you decide which one? Why?

35 ft

161 mph

-70 F200 m 30 East of North

12,200 people


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Vectors vs. ScalarsThe answer is: 200 m 30 East of North

Why is it different?

All the others can be completely describedwith only a numerical magnitude. Numberswith that property are called SCALARS.

Numbers that need both magnitude anddirection to be described are calledVECTORS.


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Notation Vectors are written as arrows.

The lengthof the arrow describes themagnitudeof the vector.

The directionof the arrow indicates thedirectionof the vector

Vectors are written in boldtext in your

book On the board we will use the notation

below

F


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Adding Vectors

Case1: Collinear Vectors


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What is the ground speed ofan airplane flying with an air

speed of 100 mph into aheadwind of 100 mph?


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Adding Collinear Vectors

When vectors are parallel, just addmagnitudes and keep the direction.

Ex: 50 mph east + 40 mph east = 90mph east


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Adding Collinear Vectors

When vectors are antiparallel, justsubtract the smaller magnitude fromthe larger and use the direction of the

larger.

Ex: 50 mph east + 40 mph west = 10mph east


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An Airplane flies north with

an air speed of 650 mph. Ifthe wind is blowing east at

50 mph, what is the speed ofthe plane as measured from

the ground?


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Adding Perpendicular Vectors

When vectors are perpendicular,just sketch the vectors in a HEAD

TO TAIL orientation and use righttriangle trigonometry to solve forthe resultant and direction.

Ex: 50 mph east + 40 mph north = ??


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Use Pythagorean Theorem to solve for R andRight triangle trig. To solve for

R


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Use the Pythagorean Theorem andRight Triangle Trig. to solve for R

and q

R Rx

2

Ry

2

tan1 Ry

Rx


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Examples

Ex1: Find the sum of the forces of30 lb south and 60 lb east.

Ex2: What is the ground speed of aspeed boat crossing a river of 5mph

current if the boat can move 20mph instill water?


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Vector Components

Vectors can be described usingtheir components.

The Componentsof a vector aretwo perpendicular vectors thatwould add together to yield theoriginal vector. Components arenotated usingsubscripts.

F

Fx

Fy


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An Airplane flies north with an air

speed of 575 mph. If the wind isblowing 30 north of east at 50mph, what is the speed of the

plane as measured from theground? What if the wind blew

south of west?


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Adding Vectors with ScaleDiagrams

When vectors are not parallel orperpendicular the only way to add

them is by drawing a SCALEDIAGRAM

Add the vectors head to tail.

Measure R and with a ruler andprotractor.


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Adding Vectors by Components

A

B


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Adding Vectors byComponents

A B

Transform vectors so they are head-to-tail.


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A BBy

Bx

Ax

Ay

Draw components of each vector...


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A B

By

BxAx

Ay

Add components as collinear vectors!


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A B By

BxAx

Ay

Draw resultants in each direction...

Ry

Rx


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A B

Combine components of answer using

the head to tail method...

Ry

Rx

R


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Adding Vectors by

ComponentsUse the Pythagorean Theorem andRight Triangle Trig to solve for R

and q

R Rx

2

Ry

2

tan1 Ry

Rx


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Examples

Find the sum of the forces140 lb

at 40 deg. North of west and 220 lb

at 30 deg north of east


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Comparing Methods

Why is the component

method a better method thanthe scale diagram method?


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