Name: ________________________________________

Vector Voyage Worksheet 1

Date: ____________________

Africa

North

America Europe

United States

Canada

Spain

England

Portugal

Cuba Atlantic Ocean

Vector Voyage Instructions

Part 1: Your ship can sail 10 squares/month. Starting from Spain and travelling west (or bearing 270), draw one vector for each month of travel using your red pencil. In what country will you make landfall? ___________ How many months will it take to reach land (how many 10-square vectors is it)?___________

Part 2: Unfortunately, the wind does not always blow the way you want! To determine how the wind effects our travel, let's include the wind vector. First, draw your ship vector, just like in part 1, using your red pencil. Now at the end of that vector, add the wind vector using your blue pencil. Now draw the resulting vector (just adding the two vectors) with your blue pencil. That's where you are when the first month ends. Now do the same for the next month and the month after that until you reach land. Remember that the wind changes, so each month you will have to add a different wind vector. The list of different winds for each month is on the following line.

Month 1: 2 squares south Month 2: 4 diagonal squares southeast Month 3: 2 squares west Month 4: No windWhere will you make landfall now? ___________ How many months to reach land (only count the solid 10-square vectors!)?___________

Start!

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Navigation: Lesson 2, Vector Voyage Activity - Worksheet 1

a t h3 am mnthtF

month 4 month 33M

USA34 Maryland2 Maine

Florida 4month

Name: ________________________________________________

Vector Voyage Worksheet 2

Date: ___________________

Africa

North

America Europe

United States

Canada

Spain

England

Portugal

Cuba Atlantic Ocean

Vector Voyage #2 Instructions

Part 3: Unfortunately, ocean currents affect boats too! Each month, you must also add a current correction vector to find your actual final position. So just like in Part 2, for each month, draw your ship vector (in red), and your wind vector (in blue) and now add on your ocean vector (in green). Now using your green pencil, draw the resulting vector from all of these (add the red and the blue and green vectors). Do this for each month until you hit land. Remember the wind and the ocean vector's will be different for each month. They are listed below.

Wind Vectors: Month 1: 2 squares south Month 2: 4 diagonal squares southeast Month 3: 2 squares west Month 4: No wind

Ocean Vectors: Month 1: 2 squares south Month 2: 4 squares west Month 3: 3 diagonal squares southwest

Where will you make landfall now? ___________ How many months to reach land (only count the solid 10-square vectors)?___________

Start!

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Navigation: Lesson 2, Vector Voyage Activity - Worksheet 2

Cuba 3month

Unit 1 Day 1Intro to vectors

Vector is a directed line segment that representsquantities such as force velocity and accelerations

VectorPoint Head

Ca b tyrmenia b

einitialTail

The length of a vector is called magnitude1J or 11811

Avector V

Examren 11811 TEKV Vz43,27 ME

ATE

Standardposition is if the initial Point is at theorginStandard Position is written in component form

Sketch I amJ L 4 67 µ

Example

Find the component form and magnitude for POT

F C3,4 and Q L 5,2p n PI Head minus tail Uwkhenth.in

L 5 3,2 4 v Vz U U UzQ.t ca.IT two pointsiiiµ VIE th Vi Uz k and youneed

to find the vectoqfg nf.rs2ra in comp form

v

Find the component form and magnitude to PJ

When P C2,6 and Q C 5 2

PIE 3 4 115041 5

Find the component form and magnitudefor PI

when D 3,4 and Q 5 2

POT L 8 6 7

11POTH 10

Equivalentictors have the same lengthand direction

show that the arrow from R C 4,2 to S C l 6

is equivalentto the arrow from F 2 1 to Q 5,3

1112511 5Rg L 3 4

POT L 3 4 3 11POT11 5 Equivalent

VectoroperationsLet it L Up Uz T L V Vz K is a scalar

real number

Itv U g Uz t L V Vz LU V g Uz Vz

I T U g Uz LV Vz LU V g Uz Uz

Scalar Multiplication KT KL U sUz L KU g kUz

Negative vectors I tu L U s uz

Exampleslet it L I 3 and 8 24,7

Find the component form of the following vectors

a Lie L 2,6 b I J L l 4 3 7

2L 1,3 L 5 4

C 2It3v d 3Itti

L 2,6 t 412,213,9 L 4 7

10,27L 7,2

OtrantoLO O this is the Zero Vector It has no direction

If 11811 1 then it is called the unitvectormagnitude

Any non zero vector can be written as a unit vector

Te I E

HTH

EXanpFind the unit vector in the direction of 8 2 3,2

HfH N3 unit vector TEE 2NENE isnt

L 3T 2F

Standard unit vectors are linear combinations usingthe vectors I Ll o and J LO I

Ait bj La b J L a b

ALI O t b LO I

La O t Lo b

aft b5Example

giventhe linear combination 2i 3J u

and the linear combination 4it6j J

find Itv

a L 2 3 8 4 4,6

Component form linear Combination

22,370 2it3jI

let D C 1,5 and Q 3,2 write POT as

a linear combination of e tj

POT L 4 37 lin combo 45 35

FindingusingDirectionAnglesIf it is given a direction angle 0 the components

of J can be computed using the formula

J L Hill Coso 11011 Sino

Exampies

Find the component form of J11811 14 0 550

7

414 cos 55 145in 55

L8.03ll.ITFind the magnitude and direction angle

given 8 4 2 57osi

HJ N29 DirectionAngle68.21 180 tan0 25

248.20 E tan E0 68.2