Help with 2D Motion: Find Plane's Direction in a 95km/h Wind

[FossilFew]

I'm looking for a little help on this one. I've been looking at it for hours.

An airplane whose air speed is 620km/h is supposed to fly in a straight path 35.0 degrees north to east. But a steady 95 km/h wind is blowing from the north. In what direction should the plane head?

I know that 95 km/h is the y value. I suspected that 620 was the resultant (not sure on this) and that the angle was 35 degrees. Looking at it I know that the angle must be greater than 35 degrees since there is a force of 95 km/h bearing down on the plane.

My thought : use a^2 + b^2 = c^2 solve for b and calculate the angle using tan-1(95/613)= 8.8

Using common sense I know that 8.8 degrees isn't right. The answer is 42.2 North of East. Any help is appreciated.

 

[Locrian]

If the plane is supposed to be heading 35 degrees north of east... but there is a wind blowing from the north (ie, it is blowing south), then the plane will have to fly at a greater than 35 degree north of east angle to compensate.

The point is, if you draw these vectors carefully, you don't have a right triangle, and can't use that formula. Make your own right triangles to solve the problem.

 

[FossilFew]

So if I draw two vectors:

vector 1

y= 620 sin 35 = 507.9
x= 620 cos 35 = 355.6


X Y
355.6 507.9
0 -95

355.6 412.9

Determine theta by using tan-1? Am I any closer to understanding it? I get 49 degrees and that isn't correct.

 

[FossilFew]

I think the 95 should be positive. I'm close with tan-1(451/508)= 41.6 degrees N of E (but it's still not 42.2 degrees N of E)

 

[Locrian]

The -95 is negative when you are writing the vector for the wind. However, when finding the length of that side of the triangle it is positive. Does it make sense that it would be treated that way?

 

[FossilFew]

Ok. I now understand that it should in should be positive. I was contradicting my initial thought. It's two vectors. Thanks for the hints.

Does my approach look correct so far?

Thanks for you help too!