Question

You are traveling on an airplane. The velocity of the plane with respect to the air is 190 m/s due east. The velocity of the air with respect to the ground is 33 m/s at an angle of 30° west of due north.

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

2.How far east will the plane travel in 1 hour?

Answer 1

velocity of the plane with respect to the air v = 190 i
velocity of the air with respect to the ground v' = - 33 * cos(30) i + 33 sin(30) j
velocity of the air with respect to the ground v' = - 28.58 i + 16.5 j

1)
The velocity of the plane with respect to the ground v " = v + v ' = 161.42 i + 16.5 j
tan^-1(16.5/161.32)
Heading of plane = 5.84 ⁰ north of East

2)
Distance = speed * time
Speed in east = 161.42 m/s
Distance = 161.42 * 1 * 60 *60 m
Distance = 581112 m