KINEMATICS IN TWO OR THREE DIMENSIONS: VECTORS
LESSON PLAN
PERIOD #3 Vectors

MATERIALS:

Vector Worksheet on Right Angle Triangle Review
Vector Worksheet on Law of Cosines and Law of Sines
Vector Worksheet on Addition and Subtraction
Vector Worksheet on Component Addition of Vectors
Notes on Calculating Vector Components - PDF FORMAT, or Word 97 Format
Vector Worksheet on Components of Vectors
Kinematics Quiz

REVIEW:

Mark and review homework assignment on Falling Bodies and Graphs
Kinematics Quiz

OBJECTIVES:

A: Vector Kinematics in Two Dimensions (Vectors and Relative Velocity)

It is expected that students will demonstrate an ability to use vector analysis to solve problems in determining velocities, displacement, and time of travel of objects.

A1.  identify scalars and vectors

A2.  identify the resultant vector and component vectors on vector diagrams

A3.  write vector equations describing the vector addition of two or more velocities or displacements

A4.  write vector equations describing the subtraction of two velocities or displacements

A5.  use graphical methods to resolve a vector into two perpendicular components

A6.  resolve a vector into components using trigonometry

A7.  use graphical methods or trigonometry to add or subtract vectors

A10.  gather and organize data, produce and interpret graphs, and determine relationships between variables

B: Vector Kinematics in Two Dimensions (Motion with Constant Acceleration)

It is expected that students will apply the concepts of motion with constant acceleration to various real-life situations.

B1.  identify situations involving the use of kinematics

B2.  solve problems involving:

•displacement •initial velocity •final velocity •average velocity •acceleration •time

Part I - Quiz :Kinematics :

• Students write the Quiz on Kinematics.

Part I - Vectors :Triginometry and X and Y Components :

• define vector
• graphical and mathematical representations of vectors

+v or -v

equation for vector addition along with the graphical representation both in one and two dimensions

v = v₁ + v₂

• tail to tip and parallelogram methods of drawing vectors
• trigonometric method of adding vectors

GUIDED PRACTICE:

Discuss/Debate questions 1 through 10.

ADDING AND SUBTRACTING VECTORS

• define the negative of vector V;
• write a vector equation describing the subtraction of two vectors; v = v₁ - v₂ which is to say v = v₁ + -v₂ So to subtract vectors just add the negative of the vector that you want to subtract. Remember that when you add the order that you place the vectors in is not important 10 = 8 + 2 or 10 = 2 + 8. But just like math when you subtract vectors order is important 6 = 8 - 2 and -6 = 2 - 8.
• use graphical methods to show the subtraction of two vectors;
• you can use tail to tail or
• you can add the negative of the vector you want to subtract
• the tail to tail method gives you the magnitude but not the direction whereas the second method provides you with both magnitude and direction
• use trigonometry to subtract two vectors;
• Multiplying a vector by a negative scalar changes the direction of the resultant vector.

VECTOR COMPONENTS

Illustrate how vectors that are not perpendicular can be added together by breaking them down into x and y components, and by using the sum of the x and y components calculate the resultant vector.

D_r = D₁ + D₂

D₁ = D_x1 + D_y1

D₂ = D_x2 + D_y2

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D_r = D_xr + D_yr

• illustrate this graphically on the board with vector diagrams.

EXERCISE:

problems #2, 4, 6, 10, 14, 18

EVALUATION:

Quiz 3.4 Vectors at the end of next lesson.