# Airplane Vector Problem: Drawing the diagram

• susan_khan
Sorry I meant I’m getting an angle of 45 when I draw my diagram not the actual angle that needs to be solved for using sine. When I add 15 and 30 based on my diagram I get 45. Is that the right angle to plug into the cosine law?Yes, that is the angle you need to solve for. You can do this using the cosine law. First, draw a right triangle with the airplane as the hypotenuse and the two vectors representing the wind at 30 degrees and 15 degrees as the other two sides. Then use the cosine law to find the angle between the wind vector and the hypotenuse. That angle is 45 degrees. f

#### susan_khan

Thread moved from the technical math forums to the schoolwork forum
An airplane has an air velocity of 500 km/h [N 30 E] and encounters a wind from [S 75 W] at 180 km/h, find the ground velocity. Make sure you draw a big, labelled diagram.
Please help! I’m understand the calculations that need to be done (cosine law then sine law for the angle) but I’m a little confused on how to draw the diagram. Could someone please help if you can ?

Do you understand the terms "air velocity" and "ground velocity"? If so, please explain them in your own words.

For the drawing, make the vertical (y) axis North, and the horizontal (x) axis East. Basically it looks like a compass with N, E, S, and W labeled for the 4 axis vectors out from the origin.

Then draw a vector from the origin out in the NE direction of the appropriate length to represent the airplane's velocity with respect to the air. Then draw a vector from the origin out in the SW direction with the appropriate length to represent the wind. Then copy that wind vector with its tail on the nose of the airplane's air velocity vector, preserving the angle and length of the wind vector. You have just drawn the vector sum of the airplane's velocity and the wind velocity, which represents the overall velocity of the airplane over the ground.

Does that make sense?

For the drawing, make the vertical (y) axis North, and the horizontal (x) axis East. Basically it looks like a compass with N, E, S, and W labeled for the 4 axis vectors out from the origin.

Then draw a vector from the origin out in the NE direction of the appropriate length to represent the airplane's velocity with respect to the air. Then draw a vector from the origin out in the SW direction with the appropriate length to represent the wind. Then copy that wind vector with its tail on the nose of the airplane's air velocity vector, preserving the angle and length of the wind vector. You have just drawn the vector sum of the airplane's velocity and the wind velocity, which represents the overall velocity of the airplane over the ground.

Does that make sense?
Yes thank you so much!!

berkeman
Yes thank you so much!!
You're welcome. I left some steps out there at the end, so you still have some work to do, but at least you now can start the diagram. You still need to think about the questions @kuruman has asked, since they go toward your intuition for how to solve problems like this.

Yes thank you so much!!
I’m getting an angle of 45 degrees is that correct?

You're welcome. I left some steps out there at the end, so you still have some work to do, but at least you now can start the diagram. You still need to think about the questions @kuruman has asked, since they go toward your intuition for how to solve problems like this.
I’m getting an angle of 45 degrees is that somewhat correct?

I’m getting an angle of 45 degrees is that somewhat correct?

To post math, you can start off just typing it into the edit window since you are new here, but as you get more experience, please use LaTeX to post math here. There is a "LaTeX Guide" link also under the Edit window.

I’m getting an angle of 45 degrees is that somewhat correct?
It's insufficient. Your answer should be in the form V km/hr [X angle Y], i.e. specify the speed and the bearing.