Velocity is Relative: Reference Frames

[DeaZ]

1. The Question Verbatim
"A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0 N of E (LETS CALL THIS VECTOR = A). The pilot heads directly for Sparta and flies at an airspeed of 160km/h. After flying 2.0 h, the pilot expects to be at Sparta but instead he finds himself 20 km due west of Sparta (LETS CALL THIS VECTOR= B) He has forgotten to correct for the wind.

1) What is the velocity of the plane relative to the air?
2) Find the velocity (magnitude and direction) of the plane relative to the ground
3) Find the wind speed and direction.
2. The attempt at a solution

-The vector connecting the origin to vector B will be called Vector C. My first problem is finding the proper angle. I know that vector A is 20deg north of east ... but I don't know how to find the angle, at the origin, for the triangle. It isn't a right-angle, and the 20deg applies to a much larger area.

The second issue I have is distinguishing what is what. From what I understand, the velocity of the plane relative to the air (question 1) is vector C. The velocity of the plane relative to the ground ... to me ... also seem to be vector C. Am I missing something here?

 

[learningphysics]

You should be able to use right triangles to find the new angle...

Draw a picture of the origin, Sparta... the line joining the origin and sparta is 320Km... it forms an angle of 20 degrees with the east axis... so you have a right triangle... hypoteneuse 320, angle 20.

But the plane ends up 20km west of sparta... draw that point... draw a line joining the origin and that point... you can draw a new right triangle... the new right triangle has the same height as the previous... but the base is 20km less... you should be able to find the new angle...