MHB Help Needed: Vectors - Calculate Plane Velocity & Direction

[JRoomer]

Please can anyone help with:

a plane has speed in still air (no wind) of 40kmh-1 and is traveling in a direction of 65 degrees bearing but there is a wind blowing at a speed of 20kmh-1 from the south east. If I is east and J is north, express the velocity p for the plane in no wind and velocity w of the wind in component form.

Then calculate the resultant velocity and magnitude and direction??

 

[skeeter]

a plane has speed in still air (no wind) of 40kmh-1 and is traveling in a direction of 65 degrees bearing but there is a wind blowing at a speed of 20kmh-1 from the south east. If I is east and J is north, express the velocity p for the plane in no wind and velocity w of the wind in component form.

bearing of 65 degrees is measured clockwise from due North = 25 degrees CCW from due East

wind from SE blows toward 135 degrees CCW from East

Air vector ...

$\vec{A}= 40\cos(25)\vec{i}+40\sin(25)\vec{j}$

Wind vector ...

$\vec{W} = 20\cos(135) \vec{i} + 20\sin(135)\vec{j}$Air vector + Wind vector = Track (resultant) vector

can you finish?