Relative And Circular Motion
Physics

Tutor: None Selected  Time limit: 1 Day 
You are on an airplane traveling 30° south of due west at 160 m/s with respect to the air. The air is moving with a speed 41 m/s with respect to the ground due north.
2)
What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east)
Hi there! Thank you for the opportunity to help you with your question!
This question can be better answered by doing vector additon. The airplane is moving 30 degrees south of west (that is, if you have the WestEast axis be your xaxis, and the SouthNorth be your yaxis, then the plane will make an angle of 30 degrees with the xaxis.) We then draw a vector with magnitude 160m/s in that direction, that is the airplane with respect to the air. Now, we must add the vector due north with magnitude 41m/s.
The xcoordinate is given by 160*cos(30 degrees) + 0 = 160sqrt(3)/2
the ycoordinate is given by 160*sin(30 degrees) + 41 = 39
And now the heading is given by the arctan of the two components. theta = arctan[39/(160*sqrt(3)/2)] = 15.72 degrees (south of due west), or 180+(9015.72) = 254.28 degrees.
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