Question

Please help... A plane heads west (180.0 degrees) at a speed of 400.0 mph. The wind's velocity is southeast (315.0 degrees) at 30. mph.

What is Ax, the magnitude of the original vector of the plane?

Answer 1

What do you mean by Ax, I didn't get it

Answer 2

Ax is the magnitude of the original vector of the plane.

Answer 3

Yes, I read it, but what does this vector mean?

Answer 4

Well I'm guessing that the equation forms a triangle. One side is west (180.0 degrees) at a speed of 400.0 mph and another is southeast (315.0 degrees) at 30. mph. I think Ax is the final vector of the triangle.

Answer 5

It is asking for the length of the unknown side

Answer 6

Using vectors, we see that the velocity vector has value 400 in the direction of x, and the wind velocity vector has value -cos(45°)*30 in the direction of x.
The y component of the wind velocity vector is sin(45°)*30
Now, we have that the vector you want is: (400, 0)-(-cos(45°)*30, sin(45°)*30)=(400+sqrt(2)*15, sqrt(2)*15) and the magnitude of the vector is: sqrt((400+sqrt(2)*15)^2+2*15^2)

Answer 7

use cosine rule to get the unknown side