January 12-13 Ms. K will stamp your homework before class starts.
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Transcript of January 12-13 Ms. K will stamp your homework before class starts.
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January 12-13
Ms. K will stamp your homework
before class starts.
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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.
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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)
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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)
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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.
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How do we measure position in two dimensions?
North
South
EastWest
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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
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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)!
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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
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Vectors on a Map 1/12/11 28
Summary:
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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.
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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
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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
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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
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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?
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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
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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
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Vectors on a Map 1/12/11 28
Summary:
How do you keep track of where you
are at?
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3.1 Keeping track of where you are
• The change in position is the velocity multiplied by the time.
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Vectors on a Map 1/12/11 28
Summary:
How do you keep track of where you
are at?
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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.
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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.
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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.
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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.
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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.
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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)
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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
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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!
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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