You are traveling on an airplane. The velocity of the plane with respect to the air is 180 m/s due east. The velocity of the air with respect to the ground is 40 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

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.

Answer 2

Last answer is wrong, but thanks for the first two.

Answer 3

For the distance you'll have to make a right triangle and solve for the missing side (x). Since the plane isn't traveling directly in the east direction it wont be exactly the m/s multiplied by one hour.