How to draw vectors of an airplane & SE wind diagram

[agentnan]

I can create/solve the math problem without any difficulties once I have diagram in place, but I am having trouble setting up the diagram so that I can visualize it. The questions is:

A novice pilot sets a plane's controls, thinking the plane will fly at 2.50 x10^2 km/h to the north. If the wind blows at 75 km/h toward the southeast, what is the plane's resultant velocity.

The diagram I have is starts with a vector going in a due north direction for 250km. At the top, I have the next vector going downward at a 45degree towards a SE direction. (see attached)


My resultant vector then would be from the tail of the first vector to the tail of the southeasterly vector.

While I can see what the answer SHOULD be...my diagram does not allow for the correct answer. Can someone please help me with what the diagram should look like and why?

Thanks so much!

 

[radou]

Again, http://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Vector_addition.png/467px-Vector_addition.png" .

 

[agentnan]

I am sure your response should help me, but I am still confused. This is the answer as I got it using the diagram I attached:
Using the Law of Cosines:
a^2 = (75)^2 + (250)^2 - w(75)(250)cos(45)
so my solution for a was 204.

For the directional, I got an answer of 15 degrees east of north. The book, however, says the answer is 75 degrees. I cannot figure out how to get their answer. Since my math appears to be correct, I am assuming that my diagram must be incorrect somehow.

Thanks...also can you let me know how to delete multiple entries? I tried the edit/delete button, but I do not see any delete options...only edit. Thanks for your patience!

 

[Doc Al]

For the directional, I got an answer of 15 degrees east of north. The book, however, says the answer is 75 degrees.

Realize that 15 degrees east of north is equivalent to 75 degrees north of east.

(I deleted the multiple entries.)

 

[MaggieW]

Same Problem

I had the same problem. I was so desperate to find the answer so I typed the question into google and found this. The book has a stupid way of finding the answer (protractor way). I'm going to ask my teacher tomorrow about this one.