## Lesson 3: Displacement in Two Dimensions

## Overview:

So far, you have learned about motion in one dimension. In this section, you will learn how to combine vectors to describe the position of an object in two dimensions. From this, you will be able to determine the object's two-dimensional displacement using different methods. This basic but important skill will prepare you for describing two-dimensional velocity and acceleration using vector addition.

## Curriculum Expectations:

**Specific Expectations:**

**B2.1**Use appropriate terminology related to dynamics, including, but not limited to: inertial and non-inertial frames of reference, components, centripetal, period, frequency, static friction, and kinetic friction.

**B2.2**Solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methods.

## Success Criteria:

- What does the length of the vector represent?
- What does the direction of the vector indicate?
- How can you read the direction [W 35 N]?
- When you draw a vector, you can choose where you want to locate the arrow, just as long as what remains the same?
- Does the order of adding vectors matter?
- What are component vectors, and describe the process of resolving vectors into component vectors.
- Describe how to add two or more vectors by using perpendicular components. Make sure to include how to find the magnitude and the direction of the resultant vector.

## Time Allocation: 2 hours

## Learning A

ctivities:**Read**pages 22 - 28 from Nelson 1.3

Vector AdditionLearn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats. |

In the playlist below, video:

- Will explain and give examples of what is a vector and how is used in math and physics.
- Will explain and give examples of vector notation.
- Will show you how to add vectors graphically using the tip-to-toe method.
- Will show you how to add vectors graphically using the parallelogram method.
- Will explain and give examples of components and magnitudes of a vector.
- Will show you how to find the components of a vector.
- Will show you how to add vectors numerically, example 1.
- Will show you how to add vectors numerically, example 2.

**Practice**question 1 on page 26.

**Practice**questions 1 and 2 on page 28.

## Task:

**Solve**questions 3, 4, 5, 6, and 10 from Nelson 1.3 Review on page 29.

*Optional Extension:*- Practice question 3 on page 28.
- Solve question 7 on page 29.

## Reflect:

How does your choice of coordinate system affect the measurements of position and displacement?