wind speed ---- x mph
(1/2)(180 - x) = 80
180-x = 160
x = 20
(1/2)(180 - x) = 80
180-x = 160
x = 20
(1/2)(180 - s) = 80 cos 50
and if e is the east component of wind velocity
(1/2) e = 80 sin 50
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 :)
speed = sqrt (77^2 +123^2)
Read it superficially, totally ignored the direction.
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.