Vectors: air speed, ground speed

[slakedlime]

[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!

 

[Astronuc]

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?

 

[slakedlime]

Thank you very much for explaining it to me. I found the answer of 60 km/h answer at this webpage:

http://dev.physicslab.org/Document.aspx?doctype=5&filename=Compilations_AAPTQuizzes_PB1999_part1.xml

It's question no. 6. However, there was no explanation. Maybe they were wrong.

 

[Astronuc]

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.

 

[slakedlime]

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