VectorsVectors

OK, so what are these OK, so what are these vector thingamajigs?vector thingamajigs? A vector is a value / measurementA vector is a value / measurement Vectors have Vectors have MAGNITUDEMAGNITUDE and and

DIRECTIONDIRECTION– Displacement, velocity, acceleration, Displacement, velocity, acceleration,

force, momentum, etc.force, momentum, etc.– As opposed to a SCALAR which only As opposed to a SCALAR which only

has magnitude (mass, temperature, has magnitude (mass, temperature, time, etc.)time, etc.)

Use an Use an ARROWARROW to to represent the valuerepresent the value

Remember…Remember…

Don’t make this harder than it Don’t make this harder than it needs to beneeds to be

We use arrows to represent ANY We use arrows to represent ANY vector to SIMPLIFY thingsvector to SIMPLIFY things

We can then use GEOMETRY / We can then use GEOMETRY / TRIG to break the vectors downTRIG to break the vectors down

EXAMPLESEXAMPLES

A car moves to the right 286 mA car moves to the right 286 m

x

y

286 m

DISPLACEMENTVECTOR

EXAMPLESEXAMPLES

A girl walks south at 0.2 m/sA girl walks south at 0.2 m/s

E

N

0.2 m/s

VELOCITYVECTOR

EXAMPLESEXAMPLES

A person pulling a rope to the left 30A person pulling a rope to the left 30° ° above the horizontal with a force of 10 Nabove the horizontal with a force of 10 N

x

y

10 N

FORCEVECTOR

30°30°

Adding VectorsAdding Vectors

A + B = B + A = R (Resultant)A + B = B + A = R (Resultant) ALWAYS add Tip To Tail (TALWAYS add Tip To Tail (T33))

x

yA

B

R

B

A

A

B

EXAMPLE:EXAMPLE:

You are crossing a river:You are crossing a river:– Current is moving at 1.2 m/sCurrent is moving at 1.2 m/s– You can swim at 0.85 m/sYou can swim at 0.85 m/s

NO CURRENT

vs+ vc= vR

Vector ComponentsVector Components

Every vector has an x and y Every vector has an x and y component (depends on component (depends on coordinates)coordinates)

x

y

A

Ax

Ay

Ax + Ay = A

Solving for Solving for ComponentsComponents

x

y

30°

A = 15 m/s

Ax

Ay

ComponentsComponents

x

y

θ

V0x

V0y

V0

Practice Problem #1Practice Problem #1

You are lost in the wilderness and You are lost in the wilderness and when you try to go and find help, when you try to go and find help, you just end up getting more lost. you just end up getting more lost. You realize you walked (from your You realize you walked (from your starting point) starting point) 264 m at 280° and 264 m at 280° and 118 m at 25° (all compass 118 m at 25° (all compass headings). headings). What is your final What is your final displacement from your start?displacement from your start?