VectorsVectors

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BellworkBellwork

►Bellwork: Do you use the “Word Bellwork: Do you use the “Word Doc” and “PowerPoints” from the Doc” and “PowerPoints” from the labs?labs?

►Bellwork class pollBellwork class poll

Representing VectorsRepresenting Vectors

►Use an arrow for vectorsUse an arrow for vectors►Parts of the vector arrowParts of the vector arrow

TailTail HeadHead

Name: the magnitude and unit of what Name: the magnitude and unit of what it it representsrepresents

ResultantResultant

►Resultant:Resultant: A vector that repesents A vector that repesents the sum of two or more vectors the sum of two or more vectors

Scalar Quantity

Vector Quantity Unit of Measurement

Distance Displacement meter (m)

Speed Velocity meter per second (m/s)

(none) Acceleration meter per second per second (m/s2)

Time (none) second (s)

Mass (none) kilogram (kg)

(none) Force Newton (N)

Vector ScalingVector Scaling

►Scaling the vector so it can be Scaling the vector so it can be represented in a convent methodrepresented in a convent method

►Use a “Use a “Scaling FactorScaling Factor””►(e.g.) 5 cm = 600 km (U.S. map)(e.g.) 5 cm = 600 km (U.S. map)

5 cm = 150 km (AZ map)5 cm = 150 km (AZ map)►Aside 1:12,000,000Aside 1:12,000,000

1:3,000,0001:3,000,000

1 cm = 35 km1 cm = 35 km1:3,500,0001:3,500,000

1 cm = 10 km1:100,000

DirectionsDirections

►North (N) North (N) (top of page)(top of page)►Northeast (NE)Northeast (NE)►East (E)East (E)►Southeast (SE)Southeast (SE)►South (S)South (S)►Southwest (SW)Southwest (SW)►West (W)West (W)►Northwest (NW)Northwest (NW)

Other DirectionsOther Directions

►UpUp►DownDown►Left Left ►RightRight►DegreesDegrees

Vector AdditionVector Addition►Head-to-Tail methodHead-to-Tail method ►Starting from where the head of Starting from where the head of

the first vector ends, draw the the first vector ends, draw the second vector second vector to scaleto scale in the in the indicated directionindicated direction

►Repeat for all vectors that need Repeat for all vectors that need to be added to be added

►From the starting point to the From the starting point to the end point, with direction, is end point, with direction, is called the resultant called the resultant

Finding Distance and Finding Distance and Resultant DisplacementResultant Displacement

►Distance – add all of the Distance – add all of the magnitudes of each vector magnitudes of each vector

►Resultant Displacement – the Resultant Displacement – the distance from the starting point to distance from the starting point to the end point the end point andand the direction the direction

Vector Vector AssignmentsAssignments

Displacement Class WorkDisplacement Class Work

►What is the scale?What is the scale?►Measure the soccer fieldMeasure the soccer field►Soccer field is about 100 m longSoccer field is about 100 m long►Scaling Factor: 4 cm = 100 mScaling Factor: 4 cm = 100 m►OR 1 cm = 25 mOR 1 cm = 25 m►OR 1:2,500OR 1:2,500

Displacement AssignmentDisplacement Assignment► 1) Starting point is the “DROP AREA”1) Starting point is the “DROP AREA”► 2) Label an “END POINT” that is not near 2) Label an “END POINT” that is not near

the drop areathe drop area► 3) DRAW and LABEL at least 15 vector 3) DRAW and LABEL at least 15 vector

arrows around the school’s campus to the arrows around the school’s campus to the end pointend point

► 4) MEASURE each of the vector arrows 4) MEASURE each of the vector arrows using a ruler (to the 0.1 cm)using a ruler (to the 0.1 cm)

► 5) CONVERT (in dominoes) your 5) CONVERT (in dominoes) your displacement vectors (cm) into meters, displacement vectors (cm) into meters, include units and direction.include units and direction.

► 6) FIND the total distance in meters by 6) FIND the total distance in meters by adding vectors together adding vectors together

► 7) DRAW the 7) DRAW the resultantresultant vector: vector:a) measure the distance from the start a) measure the distance from the start

point to point to the end point.the end point.b) convert the cm to m b) convert the cm to m