1 / 20

# Vectors - PowerPoint PPT Presentation

Vectors. You will be tested on your ability to: correctly express a vector as a magnitude and a direction break vectors into their components add and multiply vectors apply concepts of vectors to linear motion equations (ch. 2). Vector vs. Scalar.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Vectors' - shea-buckley

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Vectors

You will be tested on your ability to:

correctly express a vector as a magnitude and a direction

break vectors into their components

apply concepts of vectors to linear motion equations (ch. 2)

• Scalar units are any measurement that can be expressed as only a magnitude (number and units)

• Examples:

• 14 girls

• \$85

• 65 mph

• Vector quantities are measurements that have BOTH a magnitude and direction.

• Examples:

• Position

• Displacement

• Velocity

• Acceleration

• Force

• Graphically, vectors are represented by arrows, which have both a length (their magnitude) and a direction they point.

v = 45 m/s

d = 50 m

v = 25 m/s

a= 9.8 m/s2

• The symbol for a vector is a bold letter.

• For velocity vectors we write v

• For handwritten work we use the letter with an arrow above it. v

• Algebraically

• Vectors are written as a magnitude and direction

• v = lvl , Θ

• Example v = 25 m/s, 120o or d = 50 m, 90o

• Choose a scale

• Measure the direction of the vector starting with east as 0 degrees.

• Draw an arrow to scale to represent the vector in the given direction

• Try it! v = 25 m/s, 190o scale: 1 cm = 5 m/s

• This can be described 2 other ways

• v = 25 m/s, 10o south of west

• v = 25 m/s, 80o west of south

• Try d = 50 m, 290o new scale?

• Vector Equation

• vr = v1+v2

• Resultant- the vector sum of two or more vector quantities.

• Numbers cannot be added if the vectors are not along the same line because of direction!

• Example……

• To add vector quantities that are not along the same line, you must use a different method…

D3

D2

DT

D1

D1 = 169 km @ 90 degrees (North)

D3 = 195 km @ 0 degrees (East)

D2 = 171 km @ 40 degrees North of East

DT = ???

• On a diagram draw one of the vectors to scale and label it.

• Next draw the second vector to scale, starting at the tip of the last vector as your new origin.

• Repeat for any additional vectors

• The arrow drawn from the tail of the first vector to the tip of the last represents the resultant vector

• Measure the resultant

• d1 = 30m, 60o East of North

• d2 = 20m, 190o

• dr = d1+d2

• dr = ?

• dr = 13.1m, 61o

• Given a vector v, we define –v to be the same magnitude but in the opposite direction (180 degree difference)

• We can now define vector subtraction as a special case of vector addition.

• v2 – v1 = v2 + (-v1)

• Try this

• d1 = 25m/s, 40o West of North

• d2 = 15m/s, 10o

• 1cm = 5m/s

• Find : dr = d1+d2

• Find dr = d1- d2

v

–v

• Multiplying a vector v by a scalar quantity c gives you a vector that is c times greater in the same direction or in the opposite direction if the scalar is negative.

cV

V

-cV

• A vector quantity is represented by an arrow.

• v = 25 m/s, 60o

• This single vector can also be represented by the sum of two other vectors called the components of the original.

v = 50 m/s, 60o

sinΘ = Vy / V

Vy= V sinΘ

cosΘ = Vx / V

Vx= V cosΘ

V2 = 10 m @ 30 degrees above –x

Find: V2X =

V2Y =

V1 = 10 m @ 30 degrees above +x

Find: V1X =

V1Y =

Ө2

Ө1

But V2X should be NEGATIVE!!!

Try using the angle 150 degrees for V2

V2 = 10 m @ 30 degrees above –x

Find: V2X =

V2Y =

V1 = 10 m @ 30 degrees above +x

Find: V1X =

V1Y =

Find : V3X =

V3Y=

V3 = 10 m @ 30 degrees below +x

Try using the angle 330 degrees for V3

VX = 25m/s

VY = - 51m/s

Find V=

• ALWAYS:

Describe a vector’s direction relative to the +x axis

• ALWAYS:

Measure counter-clockwise angles as positive

• ALWAYS:

Measure clockwise angles as negative

D3

D3X

D2

D2Y

D2X

DT

D1Y

D1

D1 = 169 km @ 90 degrees (North)

D3 = 195 km @ 0 degrees (East)

D2 = 171 km @ 40 degrees North of East

DT = ???

y (km)

x (km)

We’ve Found:

DTX = 326 km

DTY = 279 km.

y (km)

For IDTI, use the Pythagorean Theorem.

For the Direction of DT, use Tan-1

x (km)

• Pg. 70, # 1, 4