Headwinds and tailwinds

Maths Age group: KS4: ratio, vectors and right-angled triangles

A plane flies through moving air. Work out what that does to its speed and why runways face the wind.

Before you start

Read or play with these Learn topics first.

Choose an airport

Latest weather report (explained in "How do you read an airport weather report?")

Name: ______________________ Date: ____________

Use the live board for this worksheet.

A plane flies at 450 kt through the air with a 50 kt tailwind. What is its speed over the ground?
Same plane, 50 kt headwind. Speed over the ground?
Find the wind at an airport on the live board. Which runway is in use, and why?
Draw the wind and the runway as a right-angled triangle. Work out the crosswind.

Ten questions on this lesson. Pupils open the link on any device. Nothing is stored about them.

Teacher notes and answers

Suggested answers. Many will vary with the live data, so check units and working. The curriculum links are a guide only.

450 + 50 = 500 kt.
450 − 50 = 400 kt.
Answers will vary. Planes take off and land into the wind, so the runway pointing most nearly into the wind is used.
Crosswind = wind speed × sin(angle between the wind and the runway). Example: 20 kt at 30° gives 20 × sin 30° = 10 kt.