Stephen Pearson
ED200
Topic: Vectors (3-1 to 3-6)
Objective: After this class, students will be able to tell the difference between vectors and scalars as well
as being able to effectively add and subtract vectors in two dimensions.
Introduction: With a class of juniors and seniors, start with the question; “Who here has a license and
drives to school?” After receiving a response, as the students what the number presented on the
speedometer represents: speed or velocity? This number represents speed, or the magnitude of the
velocity. Prompt the students to discuss a way to express the velocity of the car and let them talk about
it for 5 minutes or so.
New Material: Explain that Scalars will be used in the future, but today we are going to look at vectors,
and how their magnitudes and directions relate.
Begin by explaining in 2-D motion, every vector has an x and y value. In 3-D motion we are introduced to
z values, but these are unnecessary now. Remind your students of simple geometric and trigonomic
functions.
𝑎2 + 𝑏 2 = 𝑐 2
𝑠𝑖𝑛𝜃 =
𝑜𝑝𝑝
ℎ𝑦𝑝
𝑐 = √𝑎2 + 𝑏 2
𝑐𝑜𝑠𝜃 =
𝑎𝑑𝑗
ℎ𝑦𝑝
𝑡𝑎𝑛𝜃 =
𝑜𝑝𝑝
𝑎𝑑𝑗
Sketch three graphs on the board. One should be a 10-unit vector 30 degrees over the x-axis, the second
a 10-unit vector 45 degrees over the x-axis, and the third a 10-unit vector 60 degrees over the x-axis.
Prompt the students to take their calculators and to try and find the x and y components of each vector.
Make sure to label theta as the angle between the x-axis and the vector.
Clear the board and draw another graph on the board, this time with two vectors, both from the origin.
One should be 10-units long, 30 degrees over the x-axis, and the other 10-units long, 60 degrees over
the x-axis. Explain that in certain situation, we will be given more than one vectors, and we will need to
find to sum of them. This goes back to the independence of the x and y values of vectors.
Redraw the graph with one vector starting at the origin, and the other starting at the end of the first
one, including a horizontal dotted line where they meet. Explain that the addition of vectors can be
simplified into the addition of their x and y components.
Turn on the computer projector and bring up the following interactive problem (3.19):
http://higheredbcs.wiley.com/legacy/college/halliday/0471758019/ilw/c3_p19.htm
Work with the class to get through the problem. After you have completed the problem as a class, allow
the class to split into teams of two and go to the computers in the classroom and complete the rest of
the given interactive problems. Have the students turn in their final answers to class participation.
(Correct answers get full credit, the program will provide them)
Using the interactive software provided by the textbook company allows students to correctly visualize
each problem. Each interactive problem prompts the students to use a thorough problem-solving
method which will promote better homework and exam practice. The program also produces many
images, which is very important in physics.
Conclusion: Review with the students that scalars only have a magnitude, whereas a vector has
direction. Today was the first time that we saw that x and y values of a vector are independent. The
variables we identified today as follows: x, y, net, and θ. If we have any two of those variables, we
should be able to find the other components using simple geometric and trigonomic equations. When
adding and subtracting vectors, it is important to remember to separate vectors into x and y parts, as
those are the parts you will add to find the value together.
Homework: Students should complete:
3.1, 3.3, 3.5, 3.11, 3.15, and 3.21
From the ‘problems’ section of the text (Fundamentals of Physics, 8th Edition, 2008, edited by Halliday,
Resnick, and Walker)
Provide the following links for student’s further intuition:
The Physics Classroom- Vector Math
http://www.physicsclassroom.com/Class/vectors/
Hyper Physics- Georgia State University- Vector Operations
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html
Connexions- Vector Addition
http://cnx.org/content/m13601/latest/
Boston University- Vector Addition (This one has a really cool vector illustrator!)
http://physics.bu.edu/~duffy/java/VectorAdd.html