Vectors: air speed, ground speed

  • Thread starter slakedlime
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[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

The answer is supposed to be 60 km/h. Can someone please help or tell me where I went wrong? Thank you!
 

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Answers and Replies

  • #2
Astronuc
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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?
 
  • #4
Astronuc
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Science Advisor
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The website indicates the incorrect answer.

The air speed is due north at 120 km/h, the wind blow perpendicular (due E) at 50 km/h. Adding the vectors, gives a resultant 130 km/h, with respect to the ground.
 
  • #5
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I was thinking that, but I needed to be sure since the site didn't offer an explanation. Again, thank you! :smile:
 

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