Vector Addition and Resultant Velocity in Air Travel

[Morhas]

Simple question (I think...)

Homework Statement

A pilot takes off at a bearing [S 30deg E] with a speed of 300km/h with respect to the air. She then encompasses a wind blowing at 20km/h in the North-East direction. What will the resultant velocity be of the plane?

Homework Equations

The Attempt at a Solution

Second day of physics class. What is confusing me is that since velocity is a vector quantity, we need time to figure out how much distance was displaced. Thanks for the advice.

 

[Doc Al]

But you're not asked to find distance or displacement, only the resultant velocity of the plane with respect to the ground. You don't need time for that.

 

[Morhas]

Ahh ok. I guess I'm just not sure how to illustrate that problem with vectors, because I don't have any magnitude for them. I don't know if that is relevant to this problem, but that is really the only approach we've been taught.

 

[lukas86]

I had this problem or almost exact one back in high school. I found it easy to draw a picture, convert each vector into vertical and horizontal components...

 

[Doc Al]

I guess I'm just not sure how to illustrate that problem with vectors, because I don't have any magnitude for them.

What do you mean you don't have any magnitudes? The magnitudes are given, along with the directions. Add those two vectors any way you were taught. Either graphically or by using components.

 

[Morhas]

EDIT: I think I've got it now. I was looking for a length before not a speed. Just needed to think about it a different way. Bleh.

Thanks.

 

[Doc Al]

The lengths of the vectors are 300km/h and 20km/h. (On your diagram, just label the coordinates with the appropriate units.)

 

[Morhas]

Yeah I'm kicking myself now. It just felt weird to illustrate a speed with a line.

 

[Doc Al]

I know the feeling. I knew it would click if you thought about it long enough.