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?
what about the degrees
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
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 :)
whoops
speed = sqrt (77^2 +123^2)
Woops, just ignore my post
Read it superficially, totally ignored the direction.
wind speed ---- x mph
(1/2)(180 - x) = 80
180-x = 160
x = 20
To find the wind velocity, we need to break down the plane's velocity into its components: ground speed and wind speed.
Let's start by analyzing the ground speed of the plane. We know that the distance traveled is 80 km [N5oE] in 30 minutes. This means that the plane has traveled 80 km to the north and 80 km * sin(5°) to the east (since it's heading N5oE).
Using the relationship speed = distance/time, we convert the time to hours (30 minutes = 0.5 hours). Therefore, the ground speed of the plane is 80 km / 0.5 h = 160 km/h.
Now, let's find the wind velocity. We'll assume that the wind is blowing directly from the east (perpendicular to the plane's heading). Let's denote the wind velocity as w km/h. Since the plane's velocity is a combination of its own speed (180 km/h) and the wind speed, we can write:
180 km/h - w km/h = 160 km/h
To solve for the wind speed, we subtract 160 km/h from both sides:
180 km/h - 160 km/h = w km/h
20 km/h = w
Therefore, the wind velocity is 20 km/h from the east.