Aircraft Direction to Fly North: Solve Airplane Problem

[Throwback24]

Homework Statement

An aircraft has a cruising speed of 100 m/s. On this particular day, a wind is blowing from the west at 75 m/s.

If the pilot wishes to have a resultant direction of due north, in what direction should the plane be pointed? What will be the plane displacement in 1.25 h?

Homework Equations

The Attempt at a Solution

I answered the other two parts of the question asking for the total displacement and velocity relative to the air or something. Where do I start with this?

I know it has to do with polar positives but my textbook has no examples.

 

[LowlyPion]

Isn't it just a vector addition problem?

They give you 1 vector - the wind (direction,magnitude) and they give you the resultant (direction, but not magnitude) and they give you the plane speed magnitude but not direction.

In the X direction, It's

75 Wind = -75 for Plane = 100*Cosθ because the resultant has no X component.

So isn't θ found by the acrCos(.75) = θ where θ is with respect to the -x axis?

Then in the Y direction it's |Resultant| = 100*Sinθ

Then of course your displacement after 1.25 hrs is 1.25 * |Resultant|

 

[Throwback24]

If the wind is blowing from the west doesn't that mean it's going east? Thus positive?

acrCos(.75)

What does this mean?

Thank you.

 

[LowlyPion]

If the wind is blowing from the west doesn't that mean it's going east? Thus positive?

acrCos(.75)

What does this mean?

Thank you.

Yes the wind is going to the east, but you must fly the plane to the west against the wind at an angle to go north.

The arcCos is sometimes written as Cos^-1(.75)

Given the value of the Cosine θ, it returns the value of θ.

Go to Google and enter "arccos(.75) in degrees".

You should familiarize yourself with the inverse trig functions as they will be useful in figuring the angles in a number of these kinds of vector problems.