STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 4 (Pythagorean 

Theorem) Educator Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) EDUCATOR GUIDE

OVERVIEW

Objectives

Standards

Materials

This lesson uses real-world scenarios through which students use the Pythagorean Theorem to calculate airspeed, wind 

speed, and groundspeed. 

Students will be able to:

• Solve for one side of a right triangle when given the other two sides.

CCS.MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate 

system.

Next Generation Science Standards

Science and Engineering Practices

• Developing and using models

• Using mathematical and computational thinking

• Student Guides (one per student)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) EDUCATOR GUIDE | 3 

Lesson Modifications

Grouping Students

Steps

This lesson can be modified depending on student needs. 

Coordinates can be changed to adjust the difficulty of the 

calculations. Additional problems can be added to provide 

more opportunities for practice. 

The difficulty can be varied by allowing or prohibiting the 

use of calculators. If calculators are not used, answers will 

need to be expressed as square roots unless locations are 

added that lead to perfect squares. 

This activity is designed to be completed independently. Grouping can, however, be used if necessary. Students working 

in pairs can independently solve the problems and then compare answers to validate their solutions or find errors.

1. Use a warm-up or other method to introduce the 

students to the concept of Advanced Air Mobility 

(AAM) and the effect of weather on Unmanned 

Aerial Vehicles (UAVs). Students can read through 

the information found in the student guide as an 

introduction to this topic.

2. Review the Pythagorean Theorem with students to 

ensure they understand how to use it.

3. Distribute the student guide(s) and allow students to 

begin working.

4. As students are working, their work should be 

checked to discover if they are making errors. If they 

are, they can be shown the correct method.
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) EDUCATOR GUIDE

PART 1: SOLVING FOR GROUNDSPEED

A company uses package delivery drones to deliver its products to customers. These drones fly with an airspeed of 60

when carrying a package and 80 when not carrying a package.

1. A drone is carrying a package to be delivered to a customer. As it flies, it encounters a headwind of 8 . 

Calculate the groundspeed for the drone.

2. After dropping off the package, the drone flies back in the opposite direction. Now it is not carrying a package and 

the wind is blowing from directly behind it. Calculate the groundspeed for the drone.

3. If the drone carries a package and encounters a crosswind of 9 km/hr, what is the groundspeed?

4. Complete the following chart:

Airspeed Wind Type and Speed Groundspeed

30 Headwind of 7 23

75 Crosswind of 12 75.95

50 Crosswind of 15 52.20

45 Tailwind of 5 50

90 Crosswind of 9 90.4

40 Crosswind of 12 41.76

STUDENT ACTIVITY
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) EDUCATOR GUIDE | 5 

5. An air taxi is trying to fly to a spot that is directly east of the vertiport from which it takes off. There is a wind blowing 

from the north toward the south. When programming the drone’s flightpath (the airspeed and its direction), which of the 

three paths shown below (A, B, or C) should the programmers use? Explain why you chose the answer that you chose.

It should be programmed to fly path A. The wind will deflect the flightpath southward, so it should fly toward a point that

is north of the desired destination.

PART 2: SOLVING FOR AIRSPEED OR WIND SPEED

1. An engineer looks at the data from an air taxi and notices that it achieves a groundspeed of 53 when flying 

northward through a headwind, and 68 when it is flying southward. What is the airspeed of the taxi? Show 

your work.

For tailwind: groundspeed = airspeed + wind speed

68 = airspeed + wind speed

For headwind: groundspeed = airspeed − wind speed

53 = airspeed − wind speed

Add the two equations together:

 68 = airspeed + wind speed

+53 = airspeed − wind speed

121 = 2 * airspeed

airspeed = 60.5

Figure 3. The three possible paths for the drone’s flight. Credit: USGS
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) EDUCATOR GUIDE

2. What is the wind speed in question 1? Show your work.

3. Another air taxi has an airspeed of 50 , but it is flying with a crosswind. The pilot measures the air taxi’s 

groundspeed at 50.8 . Use the Pythagorean Theorem to calculate the wind speed.

4. Complete the following chart:

Airspeed Crosswind Speed Groundspeed

20 15 25.00

40 5 40.31

35 10 36.40

45 13 46.84

18 4 18.44
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