How do I make a compensation vector?

[yamugushi]

Homework Statement

I'm currently doing an airplane project in pre-calc, it is physics related so I put it here.
The problem is I have a plane, it's going N74W, wind is going N20E, the resultant vector is 324mph, and N67W, how do I compensate?

Homework Equations

I remember going over it once in class but I really don't want to screw it up since this project (which is a lot bigger than just this problem) is supposed to be a big part of the grade.

The Attempt at a Solution

I think I'm just supposed to make a vector go NxW, but I'm not sure how to get it.

 

[tiny-tim]

Hi yamugushi!

Relative velocities obey the law of vector addition, so draw a vector triangle

 

[kerimek]

I would suggest approaching this problem by first understanding the concept of vector addition. In this case, the plane's velocity and the wind's velocity are two separate vectors that need to be added together to find the resultant velocity. To do this, you can use the parallelogram method or the head-to-tail method. Once you have found the resultant vector, you can use trigonometry to determine its magnitude and direction.

Next, to compensate for the wind, you can use the concept of vector subtraction. This means that you need to subtract the wind's velocity vector from the resultant velocity vector to find the actual velocity of the plane. This will give you a new vector that represents the plane's actual velocity and direction.

To represent this in a compensation vector, you can use the opposite direction of the wind's velocity vector with the same magnitude. This will give you a vector that, when added to the original plane's velocity vector, will result in the desired resultant vector of 324mph and N67W.

In summary, to make a compensation vector, you need to use vector addition and subtraction to find the resultant vector and the direction of the wind's effect on the plane's velocity. Then, use the opposite direction of the wind's velocity vector with the same magnitude to create the compensation vector. I hope this helps!