Question

A plane is capable of flying 180 km/h in still air. The pilot, Sofia, takes off from an airfield and heads due north according to the plane’s compass. After 30 minutes of flight time, Sofia notices that, due to the wind, the plane has actually travelled 80 km [N5oE]. What is the wind velocity?

Answer 1

wind speed ---- x mph
(1/2)(180 - x) = 80
180-x = 160
x = 20

Answer 2

what about the degrees

Answer 3

I think if s is the south component of the wind velocity
(1/2)(180 - s) = 80 cos 50
and if e is the east component of wind velocity
(1/2) e = 80 sin 50

Answer 4

180 - s = 160 cos 50 = 103
s = 77
e = 160 sin 50 = 123
tan angle south of east = 77/123 = .626
angle of wind flow south of east = 32 deg
NOW that is the direction the wind WENT
Most of us think about where the wind is FROM
that is 32 degrees North of West :)
speed = sqrt (77^2 =123^2)
(math people may not think that way :)

Answer 5

whoops
speed = sqrt (77^2 +123^2)

Answer 6

Woops, just ignore my post
Read it superficially, totally ignored the direction.