Module 2 Lesson 2

Module 2—Motion in Two Dimensions

Lesson 2—Vector Components and Cartesian and Navigational Vector Directions

Get Focused

While booking a round-trip air ticket to Vancouver to go skiing at Grouse Mountain, you notice that it will take 1 h and 28 min to get from Calgary to Vancouver and that it will only take 1 h and 20 min to fly back. Why do you think it takes 8 min more to get there than it does to get back? The distance between Calgary and Vancouver doesn’t change. You are flying on the same aircraft at exactly the same speed (approximately 750 km/h, relative to the air) both ways. What could be going on?

vector diagram: a diagram using vectors to show motion

Vector diagrams may instead be used to show forces, fields, or momentum.

On both trips, your air velocity and distance of travel are identical. The time is different, however, because of the wind velocity. When you consider the air velocity (how fast the plane moves in the air) and the wind velocity together, you are able to show that the plane has a greater “ground velocity” when it flies toward the east. Here are the vector diagrams demonstrating that the magnitude of the ground velocity is greater when the plane travels from Vancouver to Calgary—even if the wind velocity and air velocity have a constant magnitude.

Travelling from Calgary to Vancouver:

Travelling from Vancouver to Calgary (8 min faster):

In aviation, wind velocity describes how fast the wind is moving relative to the ground. In the two previous cases, the wind velocity is constant. Air velocity, on the other hand, is a measure of how fast the plane moves relative to the air (controlled by the jet engines). And finally, ground velocity describes how fast the plane moves relative to the ground (a combination of air velocity and wind velocity).

In this lesson you will explore the following essential questions:

How do you mathematically determine the magnitude and direction of the sum of two vectors, such as air velocity and wind velocity, for a flying plane?
How do you calculate the components of the two vectors to be added when given the magnitudes and directions?

Module 2: Lesson 2 Assignments

Your teacher-marked Module 2: Lesson 2 Assignment requires you to submit a response to the following:

Try This—TR 1, TR 2, TR 3, TR 4, TR 5, and TR 6
Discuss

You must decide what to do with the questions that are not marked by the teacher.

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.