Answer
65km/h
Work Step by Step
Call east the positive x direction and north the positive y direction.
Let P denote the Plane, A the Air, and G the Ground. The pair “PG”, for example, represents the plane’s motion relative to the ground.
$$ \vec{v_{PG}} = \vec{v_{PA}} + \vec{v_{AG}} $$
The speed of the plane relative to the air is given as 185 km/h, and the speed of the plane relative to the ground is 135 km/h. The plane’s velocity relative to the ground is at 285 degrees.
Equate the y components of the velocity vectors.
$(135 km/h)(sin 285 ^{\circ}) = -185 km/h + v_{AG, y}$
The wind’s velocity relative to the ground has a y-component of 54.6 km/h.
Now consider the x components of the relative velocity equation.
$(135 km/h)(cos 285 ^{\circ}) = 0 km/h + v_{AG, x}$
The wind’s velocity relative to the ground has an x-component of 34.9 km/h.
The magnitude of the wind's velocity is $v = \sqrt {34.9^2 + 54.6^2} = 65km/h$
