Physics – Chapter 3-1 Introduction to Vectors St. Augustine Preparatory School September 4, 2015

Two dimensional motion Previously in Chapter 2 we talked about objects moving left/right or up/down or ahead/backwards, but we never combined more than one dimension. Although this is a great place to start, most of the motion in our world that we want to describe is at least two dimensional.

Terminology Scalar Quantity: Quantity that has magnitude (a number) but no direction. Ex. Speed, distance Vector Quantity: Quantity that has both magnitude and direction Resultant: The answer found by adding two vectors

Vector Notation We show that a quantity is a vector by drawing an arrow above its symbol in a formula (example: v)

Drawing Vector Diagrams We use arrows to draw vector diagrams Arrow length should represent the quantity of an arrow in comparison to the rest Arrows are drawn “tip to tail”

Drawing Vector Diagrams Example: Mary walks 5 km north before turning and walking 12km east. Draw the vector diagram for Mary’s walk.

Drawing Vector Diagrams Example: Mary walks 5 km north before turning and walking 12km east. Draw the vector diagram for Mary’s walk. 12km 5km

Qualities of Vectors Vectors can be added in any order. Consider the path of a runner below.

Finding the resultant vector The resultant vector is found by adding two vectors. If the vectors make a 90° triangle, we will use the Pythagorean Theorem (a2 + b2 = c2) Example: Mary walks 9m north and 6m east. What is Mary’s displacement?

Finding the resultant vector Example: Mary walks 9.0m north and 6.0m east. What is Mary’s displacement? We want to calculate the length of the red vector 6.0m 9.0m

Practice Problems 1) Mary walks 13.3 m east and 7.0m north. What is Mary’s displacement? 2) Mary walks 1.32km south and then 4.2km east. What is Mary’s displacement?

Direction of the Resultant Positive and negative is no longer going to be effective in describing direction. Example: The orange resultant vector is in a north direction (positive) and a west direction (negative) so would it be positive or negative?

Using the tangent (tan) function Trigonometry: θ (called theta) is the angle in degrees (Make sure your calculator is set to degrees) tan-1 is the inverse function of tan

Finding the resultant vector Example: Mary walks 9.0m north and 6.0m east. What is Mary’s displacement? Find the angle of Mary’s displacement We want to calculate the length of the red vector 6.0m 9.0m θ

Practice Problem Mary walks 7.6km south and 3.9km east. What is the magnitude and angle of Mary’s displacement?