Vectors: air speed, ground speed

[SOLVED] Vectors: air speed, ground speed

I'm having trouble drawing the diagram for this question.

Homework Statement

An airplane with air speed 120 km/h is heading due north in a wind blowing due east at 50 km/h. What is the ground speed of the plane?

Homework Equations

Pythagoras theorem.

The Attempt at a Solution

I've attached my version of the diagram with this message. I used the Pythagoras theorem since the wind blowing due east and the plane headed north meet at 90 degrees.

ground speed = sq. root {(120^2 + 50^2)}
= 130 km/h

Attachments

• vector.jpg
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Last edited:

Astronuc
Staff Emeritus
ground speed = sq. root {(120^2 + 50^2)}
= 130 km/h
That is correct. The vectors are additive and the Pythagorean theorem applies since the wind is blowing due E of the plane traveling N.

If the plane was just taveling due north with a wind speed of 120 km/h in still air, its ground speed would be 120 km/h. Only if there was a head wind of 60 km/h would it's ground speed by 60 km/h.

Where did one find that the answer would be 60 km/h?

Astronuc
Staff Emeritus
I was thinking that, but I needed to be sure since the site didn't offer an explanation. Again, thank you! 