Module 2—Motion in Two Dimensions

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resultant: a vector sum of two or more other vectors

 

parallelogram method: a method of adding vectors, where the two vectors’ tails start at the same point and define adjacent sides of a parallelogram

 

The diagonal of the parallelogram that starts where the tails meet is the resultant.

 

tip-to-tail method: a method of adding vectors where the second vector begins at the end (tip) of the first vector

 

The resultant is the vector from the tail of the first vector to the tip of the second.

There are two methods for graphically constructing the sum of two vectors, which is referred to as the resultant:

Both methods can be used to determine the velocity of the canoe and the velocity of the water that was used in the previous example. The resultant in the case of the canoe crossing the river would be the observed velocity of the boat. Both methods can be used to add more than two vectors by first adding any two vectors and then adding their resultant to a third vector using the same method.

 

Adding Two-dimensional Vectors—Tip-to-Tail Method

 

Lesson 1 Lab: Graphical Vector Addition

 

Introduction

 

This simulation lets you see the addition of vectors using the tip-to-tail method and the parallelogram method in turn.

 

You can learn more about the simulation and how to use it by reading the Show Me found at the top of the simulation screen.

 

Method 1: Tip to Tail

 

Recall the Focus

 

How can two vectors be added graphically using the tip-to-tail method of vector addition?

 

Open the Vector Addition: Graphical simulation; then continue with the procedure.

 

Procedure

 

The simulation will be used to demonstrate the tip-to-tail method of vector addition.

There is an easy way to remember in which direction to draw the resultant arrow. Think of the two vectors as one displacement following another. The resultant is the overall (net) displacement, from the point where the first displacement starts to the point where the second displacement finishes.

Observations and Analysis

 

LAB 1. Using the simulation, create the following vectors. Then identify which resultants are correct and which are incorrect.

 

a.
b.

 

 

 

 


 

c.
d.


e.
f.


g.
h.


 

Module 2: Lesson 1 Assignment

 

Remember to submit the answer to LAB 2 to your teacher as part of your Module 1: Lesson 2 Assignment.

 

LAB 2. Sketch by hand the tip-to-tail method of vector addition and the resultant vector for the following vectors. Use the Vector Addition: Graphical simulation to verify your answers.

 

a.


 

b.


 

c.


 

d.


 

Method 1 Summary

 

How can two vectors be added graphically using the tip-to-tail method of vector addition?

 

Vectors are added by placing the tail of the second vector at the tip of the first vector. The sum (resultant) is the vector that shares the first vector’s tail and the second vector’s tip.