Question

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 40.0 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).(East of due North). 3) How far east will the plane travel in 1 hour?

Answer 1

1. Vpa = 180m/s. @ 0 deg.
  Vag = 40m/s @ 120 deg,CCW.


Vpg = Vpa + Vag,
 Vpg = (180 + 40cos120) + i40sin120,
  Vpg = 160 + i34.64,
 Vpg=sqrt((160)^2 + (34.64)^2)=163.7m/s.

2. tanA = Y / X = 34.64 / 160 = 0.2165,
  A = 12.2 deg,CCW. = 12.2deg. North of East.

3.  1 hr = 3600s. d = Vt = 163.7m/s * 3600s = 589,320m.

hope this helps