You are traveling on an airplane. The velocity of the plane with respect to the air is 110.0 m/s due east. The velocity of the air with respect to the ground is 39.0 m/s at an angle of 30° west of due north.

Question

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

I'm just gonna guess:

1) 100.038888m/s
2) 77.0000 degrees East of due North
3) 360140.040000m

Answer 2

1. Vr = 110m/s[0o] + 39[120o].
X = 110 + 39*Cos120 = 90.5 m/s.
Y = 39*sin120 = 33.8 m/s.
Vr = 90.5 + 33.8i = 96.6m/s[20.5o]N. of E.

2. A + 20.5 = 90.
A = 69.5o E. of N. = 69.5o CW from +Y-axis.

3. d = Vr*T*sin A = 96.6*3600*sin69.5 = 325,737 m. = 325.74 km.