Part B: Kinematics in 2D ---------------------------------------------------------------------------------------------------------
In this section it is assumed that students understand the basic terminology used to describe motion. We add to this by introducing two dimensional vector analysis techniques including scale diagrams, components, and trigonometry. I have chosen to focus on vector addition methods (rather than subtraction) so the problems will be those of total displacement and relative motion (in perpendicular cases to keep the mathematics more trivial). Components will be of particular use when approaching projectile motion, the analysis of which was my objective for this portion of the course.
00 - Introduction
To introduce the need for additional methods to analyze motion problems I begin with a few examples on the board.
1. An object moves from a position 3 m [N] of home to a position 10 m [N] of home. What was their displacement?
2. An object travels 3 m [N] and then another 10 m [N]. Determine the total displacement.
These two examples have us review some challenging differences in terminology and can be solved with diagrams and intuition as well as algebraically.
I then pose a 2D problem:
3. An object travels 3 m [S] and then another 4 m [E]. Determine the total displacement.
The students can use the previous warm up problems to develop a solution and can begin to appreciate the complexity of the solution.
08 – 2D Vectors and Scale Diagrams
Introduces students to methods for properly identifying and drawing the angle of a 2D vector as well as how to appropriately represent the length using scales.
Basic vector addition methods and problems and discussed.
*Additional worksheets to practice diagrams (and extend ideas to subtraction) are included
09 – 2D Vectors Trigonometry and Components (2 Days)
Day 1: Components
Breaks 2D vectors into horizontal and vertical components and introduces a method of T-Charts to help students keep information organized. The advantage with this method is you can handle any number of vectors and the mathematics is never more complicated than introductory grade 10 trigonometry.
Day 2: Trigonometry
This method has limitations of only working with problems involving 2 vectors and a resultant (or 3 vectors if the resultant is the zero vector) however it is often faster in those cases. Students will be presented with options to apply the cosine law and sine law to problems. May wish to introduce the ambiguous case of sine law or select your problems carefully.
10 – Adding Velocity Vectors
While the previous lessons focus mainly on applications involving displacement, it is important that students understand that these methods work for all vectors. Relative motion is introduced as another example of where the 2D vector skills that students have been working on can be applied.
11 – Projectile Motion with Horizontal Launch (2 days)
Day 1: An investigation sheet is provided that pulls together the skills of this course thus far. Students analyze the trajectory of a projectile by reading points off an x-position, y-position graph to create separate position-time graphs for each component. They utilize velocity vectors and the methods from scale diagrams to estimate the velocity of each component in order to create separate velocity-time graphs for each component. They then recall their studies of motion graphs to draw conclusions about the motion of each component – that the x-component undergoes uniform motion and the y-component undergoes uniformly accelerated motion.
Day 2: Students are guided through several examples for the cases of horizontal launch. They begin each by setting up x- y- component charts to keep themselves organized.
12 – Projectile Motion at an Angle
Students are guided through several examples for the cases of non-horizontal launch. The importance of direction for the y-component is emphasized.
This marks the end of the 1D Kinematics portion. At this point I provide students with a review package (includes answers and solution key) and a test.