Vector Problem (Please Help)

A commercial pilot must fly from Atlanta to Chicago on a bearing of 340º at a speed of 320 knots. However, the plane must battle a crosswind coming at 34 knots on a bearing of 22º.

A) Sketch a vector diagram to show the plane's heading (p), the wind speed (w), and the desired resultant (r).

B) Determine the bearing and speed the pilot should use to stay on course and on time.

If you like to help and could list the steps to how you got the answer it would be GREATLY appreciated. I have a hard time understanding this type of vector problem.

Re: Vector Problem (Please Help)

Well, I would suggest that you start by actually **doing** what it says to do- "Sketch a vector diagram". While it isn't absolutely necessary, it is probaby best to set this up as if it were on a "compass rose"- with "north" upward on your paper. Now draw a line at "a bearing of 340º (that would be 360- 340= 20º to the left of straight up) representing the speed by making its length "320" in whatever units you want. Draw a little "arrowhead" at the tip of that to indicate direction. That is the "desired resultant". Draw a line representing the wind at 22º (22 degrees to the right of straight up) with length 34 of the same units. Connect the tips of those two "vectors". That last line is the "plane's heading".

Notice that gives you a triangle. One side of the triangle is 20 degrees to the left of north, another 22 degrees to the right so the angle between them is 20+ 22= 42º and those sides have lengths 340 and 34 (units of "knots" but you can treat them like lengths). That is, you have a triangle with the lengths of two sides and angle between them. You can use the cosine law, $\displaystyle c^2= a^2+ b^2- 2ab cos(C)$ (where C is the angle opposite side c), to find the "length" of the third side. You can then find the other two angles using the sine law: $\displaystyle \frac{sin(A)}{a}= \frac{sin(B)}{b}= \frac{sin(C)}{c}$.

Re: Vector Problem (Please Help)