January 12-13 Ms. K will stamp your homework before class starts.

January 12-13

Ms. K will stamp your homework

before class starts.

Agenda:• Homework Check

• Review Lab 3A

• VVMS Scavenger Hunt

• Keeping Track of Where You Are

• Vectors on a Map

• Practice

• Homework

Learning Goals:

• Describe an object’s position relative to a reference point.

• Differentiate between velocity and vectors.

Homework Check(3.1 Position on the Coordinate Plane)

1. You are given directions to a friend’s house from your school. They read: “Go east one block, turn north and go 4 blocks, turn west and go 1 block, then go south for 2 blocks.” Using your school as the origin, draw a map of these directions on a coordinate plane. What are the coordinates of your friend’s house?

Friend’s House (0, +2)

2. A dog starts chasing a squirrel at the origin of a coordinate plane. He runs 20 meters east, then 10 meters north and stops to scratch. Then he runs 10 meters west and 10 meters north, where the squirrel climbs a tree and gets away.

a. Draw the coordinate plane and trace the path the dog took in chasing the squirrel.

Dog Scratched (+2, +1)

Squirrel Escaped (+1, +2)

3. Does the order of coordinates matter? Is the coordinate (2, 3) the same as the coordinate (3, 2)? Explain and draw your answer on a coordinate plane.

Yes, order matters! The coordinate (2, 3) shows a point that is 2 to the right and 3

up, while (3, 2) shows a point that is 3 to the

right and 2 up.

How do we measure position in two dimensions?

North

South

EastWest

Classroom Scavenger HuntFind the starting points in the class. Your ending point is listed on the table below. Use a meter stick to write the directions (coordinates) on how to get to the final destination.

Origin Point Coordinates Ending Point

A Door to Courtyard

B Flag

C Projector Screen

D Pencil Sharpener

E Clock

F Raspusha

G Closet #12

Valley View Scavenger Hunt

Starting Point Directions (Coordinates) Ending Point

Room 136 (16, -51) (8, -2)

Room 143 (-44, -7) (2, -2)

Room 101 (-22, 1) (-11,1)

Room 257 (-1, 5) (-40, 2)

The Hive (-23, -12) (-3, 1)

Room 133 (-8, -3) (-11, 10)

Room 111 (-4, 7) (-3, 33)

Always move along the x-axis (west, east) before the y-axis (north, south)!

Table of Contents

Date Topic Page

1/6/11 Position on the Coordinate Plane 26

1/11/11 Position and Velocity 27

11/12/11 Vectors on a Map 28

Vectors on a Map 1/12/11 28

Summary:

3.1 Forward and backward

• Many variables can be positive or negative. • These include position, speed, and force. • These variables are called vectors because

they can have a value and a direction.

We use the term velocity to mean speed with direction.

What is the difference between VELOCITY and a VECTOR?

(left-side spread #28)

VELOCITY VECTOR

Both are variables

Both have values

that change

Both tell direction

+, -

Examples: position,

force, velocity

Indicates Speed (distance/time) with direction

+2 or -2

+10 cm

-10 cm

+2 meters/second

-2 cm/second

Speed, Vector, or Velocity?

+2 meters/second

10 km/hour

-15 cm

+900 miles

+4 inches

65 mph

- 28 cm/second

+4 kmh

Velocity

Speed

Vector

Vector

Vector

Speed

Velocity

Velocity

3.1 Keeping track of where you are

• Sojourner is a small robot sent to explore Mars.

• It landed on Mars in 1997.

• Where is Sojourner now?

Watch Video

3.1 Keeping track of where you are• Sojourner keeps track of its velocity vector and

uses a clock.• Suppose Sojourner moves forward at 0.2 m/s for

10 seconds.

What is Sojourner’s velocity? +0.2 meters/second+0.2 meters/second

What is it’s change in position in 10 seconds?

D

V T

A “change in position” is another way of saying distance.

Distance = velocity x time

Distance = 0.2 m/s x 10 sec

Change in Position = +2 meters

3.1 Keeping track of where you are

• Suppose Sojourner goes backward at 0.2 m/s for 4 seconds.

What is Sojourner’s velocity?

What is Sojourner’s change in position?

-0.2 m/s * The value is negative (-) because it is moving

backwards

D = (-0.2 m/s) x 4 sec

Change in Position = -0.8 metersD = V x T

Vectors on a Map 1/12/11 28

Summary:

How do you keep track of where you

are at?

3.1 Keeping track of where you are

• The change in position is the velocity multiplied by the time.

Vectors on a Map 1/12/11 28

Summary:

How do you keep track of where you

are at?

3.1 Keeping track of where you are

• Each change in position is added up using positive and negative numbers.

• Sojourner has a computer to do this.

Vectors on a Map 1/12/11 28

Summary:

How do you keep track of where you

are at?

Each change in position is added up using + and - numbers.

3.1 Maps and coordinates

• If Sojourner was crawling on a straight board, it would have only two choices for direction.

• Out on the surface of Mars, Sojourner has more choices. The possible directions include north, east, south, and west, and anything in between.

3.1 Maps and coordinates• Sojourner’s exact position can be

described with two numbers.• These numbers are called coordinates.

• This graph shows Sojourner at coordinates (4, 2) m.

3.1 Maps and coordinates

• The graph can also show any path Sojourner takes, curved or straight.

• This kind of graph is called a map.

• Street maps often use letters and numbers for coordinates.

3.1 Vectors on a mapSuppose you run east for 10 seconds at a speed of 2 m/s.

Then you turn and run south at the same speed for 10 more seconds.

Where are you compared to where you started?

D = T x V

First change in position: 10 sec x 2 m/s = 20 meters (East)

Second change in position: 10 sec x -2 m/s = -20 meters (South)

Final Position: (+20 meters, -20 meters)

PracticeA train travels at 100 km/h heading east to reach a town

in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?

Looking for: Position (Distance)

Given: Velocity vectors (speed)

Time

Formula: D = T x V

First change in position: 4 hours x 100 km/hour 400 km

Final Position: (+400 km) + (-200 km) = +200 km The train is 200 km east of where it started

Second change in position: 4 hours x -50 km/hour -200 km

PracticeA ship needs to sail to an island that is 1,000 km south

of where the ship starts. If the captain sails south at 30 km/h for 30 hours, will the ship make it?

Looking for: Position (Distance)

Given: Velocity vector (speed)

Time

Formula: D = T x V

First change in position: 30 hours x 30 km/hour 900 km

Final Position: The ship is 900 km south of where it started. The island is still 100 km away. NO!

Wrap Up

1. Summary: How are vectors, velocity, and speed different? How are they the same?

2. Homework: 3.1 Vectors on a Map

(Due: F 1/14 or T 1/18

3. Double Flipper: VVMS Scavenger Hunt

3.1 Vectors on a Map