January 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 Hunt Find 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 PointCoordinatesEnding 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 PointDirections (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 DateTopicPage 1/6/11 Position on the Coordinate Plane 26 1/11/11Position and Velocity 27 11/12/11Vectors 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 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 Speed Velocity

3.1 Keeping track of where you are Sojourner is a small robot sent to explore Mars. It landed on Mars in 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 What is it’s change in position in 10 seconds?

D VT 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 meters D = 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 map Suppose 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)

Practice A 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

Practice A 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