Question

You are traveling on an airplane. The velocity of the plane with respect to the air is 140 m/s due east. The velocity of the air with respect to the ground is 34 m/s at an angle of 30° west of due north.

1)What is the speed of the plane with respect to the ground?

2)What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

3)How far east will the plane travel in 1 hour?

Answer 1

just add the vectors:
v = <140,0> + <-17,29.4> = <123,29.4>
so the speed is |v| = 126.47

the heading is 90-θ where tanθ=29.4/123

the eastward speed is |v|cosθ

Answer 2

1. 30o W. of N. = 90+30 = 120o CCW from +X-axis.
V = 140 + 34[120o].
V = 140+34*Cos120 + i34*sin120 = 123 + 29.4i = 126.5 m/s[13.5o]N. of E.