# Vector Addition: Determining the Displacement Between Two Points in Your School

#### Summary

In this physics indoor lab students calculate the displacement from one corner of the school to the other. They complete this task by using a meter stick and recording the distances and directions needed to get there. Once all of the distances and directions are recorded, the students draw a to-scale map using vectors. Once the entire map is completed they are then instructed to calculate the displacement and direction of corner to corner of the school.

## Learning Goals

Learning Goals:

1. Use data collection to solve a problem.

2. Successful transition from one-dimensional motion to two-dimensional motion.

Concepts:

1. The students will further develop the concept of adding vertical and horizontal vectors to determine displacement.

2. The concept of components can be used to determine displacement is reinforced.

Vocabulary Development:

Components

Resultant

1. Use data collection to solve a problem.

2. Successful transition from one-dimensional motion to two-dimensional motion.

Concepts:

1. The students will further develop the concept of adding vertical and horizontal vectors to determine displacement.

2. The concept of components can be used to determine displacement is reinforced.

Vocabulary Development:

Components

Resultant

## Context for Use

This lab based activity is designed for a regular paced 12th grade physics course. It is currently used as a transition between one-dimensional and two-dimensional motion, but could be used as an assessment at the end on the introductory section of two-dimensional motion. The set-up and clean-up is extremely easy. All that is needed is one meter stick per group, graph paper for each student, and a calculator. The lab can be designed for a class of any size. I encourage the students to differ in their paths from one corner of the school to the other. Without the extension this activity should take 1-class period (50mn) to complete and graph. It should take 1 additional day for discussion and calculation. Add 1 more day for the extension.

Prior Knowledge

1. One-dimensional motion

2. Basic Graphing Skills

3. Trigonometry (sine, cosine, tangent)

Prior Knowledge

1. One-dimensional motion

2. Basic Graphing Skills

3. Trigonometry (sine, cosine, tangent)

**Subject**: Physics:General Physics:Vector Algebra

**Resource Type**: Activities:Lab Activity

**Grade Level**: High School (9-12)

## Description and Teaching Materials

To keep this activity easy, I give each group a meter stick and tell them to record the distance from the front to the back doors of the school. They are instructed to only use vertical and horizontal measurements. Once this is completed, they are instructed to graph the results to-scale (you may need to teach this) using vectors on the graph paper. As homework, the students are to calculate the distance and attempt to determine the displacement with direction.

The following day the activity continues with a short discussion guided by the students about the previous day. A quick review of displacement should be completed and the instructor should attempt to, "seek advice" from the students in terms of determining the displacement. The students generally come up with an idea similar to, "making a triangle." Ask the students, "what is the best triangle to work with?" Answer: Right triangles. Lead students towards combining similar vectors. Get students to add all horizontal vectors and then all vertical vectors to create the "components." Introduce terminology of components and lead into "resultant." Solve for resultant (displacement) using trigonometry. Remind students vectors have both magnitude and direction and once magnitude has been calculated show students how to calculate direction in 2-dimensions (trigonometry).

Possible Extension

I have also brought the blueprints into the classroom and made the students determine the actual displacement and calculate percent error.

The following day the activity continues with a short discussion guided by the students about the previous day. A quick review of displacement should be completed and the instructor should attempt to, "seek advice" from the students in terms of determining the displacement. The students generally come up with an idea similar to, "making a triangle." Ask the students, "what is the best triangle to work with?" Answer: Right triangles. Lead students towards combining similar vectors. Get students to add all horizontal vectors and then all vertical vectors to create the "components." Introduce terminology of components and lead into "resultant." Solve for resultant (displacement) using trigonometry. Remind students vectors have both magnitude and direction and once magnitude has been calculated show students how to calculate direction in 2-dimensions (trigonometry).

Possible Extension

I have also brought the blueprints into the classroom and made the students determine the actual displacement and calculate percent error.

## Teaching Notes and Tips

Be sure students are measuring in straight lines.

You may need to review basic trigonometry (soh cah toa) and Pythagorean Theorem.

This is a good intro or review to basic two-dimensional motion. Previously lecture based, now has developed into a guided inquiry lab activity.

You may need to review basic trigonometry (soh cah toa) and Pythagorean Theorem.

This is a good intro or review to basic two-dimensional motion. Previously lecture based, now has developed into a guided inquiry lab activity.

## Assessment

If used as an introduction to two-dimensional motion, it is gone over and refined as a class. I am sure they hand it in with the chapter homework at the end of the chapter, but we work towards getting problems right throughout the chapter.

If used as an assessment, one could easily grade it based on data collection, graphing, and calculation of displacement.

If used as an assessment, one could easily grade it based on data collection, graphing, and calculation of displacement.

## Standards

9-12.I.B.2 - The student will distinguish between qualitative and quantitative data.

9-12.I.B.3 - The student will apply mathematics and models to analyze data and support conclusions.

9-12.I.B.3 - The student will apply mathematics and models to analyze data and support conclusions.