How Can a Pilot Adjust Course for Wind to Maintain a Westward Path?

[CaptainofIron]

Hello I am new to this forum and I am desperate, I cannot figure this out, my professor gives us four assignments a year, on subjects that she will not lecture on at all and we have to read and find out on our own and right a report on it and then do four problems she chooses, well in theory I understand completely, but when I get to the 2d and 3d I really get confused and can't solve the problems, really frustrating not having any notes to look over. Here is the problem I am getting stuck on.

An airplane Pilot sets a compass course due west and maintains an airspeed of 220km/h. After flying for .500 hours, the pilot finds the plane over a town 120km west and 20km south of the planes starting point. A) Find the wind velocity(magnitude and direction). B) If the wind velocity is 40km/h due south, in what direction should the pilot set the course to travel due west? Use the same airspeed of 220km/h

please help. Thanks

 

[CaptainofIron]

I have tried the pythagorean theorum to try to solve for the magnitude of the wind, and the direction and I get a plausable answer but it never is the same as in the back of the book. I know that it probably isn't a right triangle. but I still can't figure this problem out after overloading my brain for almost 8 hours. The only equations my book gives is this one:
Velocity P/A= Velocity A/B+ Velocity P/B and that really doesn't help. either this book sucks or I am not getting it.

 

[wais]

Hi there,

I can understand your frustration with not having any notes to refer to for this topic. 2D and 3D relative velocity can be a challenging concept to grasp, but with some practice and understanding, you can definitely master it.

In this problem, the key is to understand the concept of relative velocity. Relative velocity is the velocity of an object with respect to another object. In this case, the airplane's velocity is relative to the ground, and the wind's velocity is relative to the airplane.

To solve this problem, we can use the formula: Vab = Va - Vb, where Vab is the relative velocity of object A with respect to object B, Va is the velocity of object A, and Vb is the velocity of object B.

A) So, in this problem, the airplane's velocity with respect to the ground is 220km/h due west. We can represent this as Vag = 220km/h due west. Now, we need to find the wind's velocity with respect to the airplane, which we can represent as Vwa. We know that the airplane's final position is 120km west and 20km south of its starting point. This means that the wind's velocity has a component in the west direction and a component in the south direction. We can represent this as Vwa = Vwx + Vwy, where Vwx is the component of the wind's velocity in the west direction and Vwy is the component of the wind's velocity in the south direction.

Now, using the formula Vab = Va - Vb, we can say that Vag = Vwa - Vwg, where Vwg is the velocity of the wind with respect to the ground. We know that the airplane's velocity with respect to the ground is 220km/h due west, and the wind's velocity with respect to the ground is 40km/h due south. So, we can write the equation as 220km/h due west = (Vwx + Vwy) - (40km/h due south). Solving for Vwx and Vwy, we get Vwx = 220km/h and Vwy = 40km/h. Therefore, the wind's velocity is 220km/h due west and 40km/h due south.

B) Now, we need to find the direction the pilot should set the course to travel due west. We know that the wind's velocity is 220