An airplane pilot flies due west at a speed of 216 km/hr with respect to the air. after flying for a half an hour, the pilot finds themselves over a town that is 119 km west and 27 km south of their starting point.

a- determine the magnitude of the velocity of the wind with respect to the ground.
(include units with the answer)

b-determine the direction of the velocity of the wind with respect to the ground measured as west from the south.

speed wind  Vw = 54.04 km / h   θ = 87.9º

Explanation:

We have a speed vector composition exercise

In the half hour the airplane has traveled X = 108 km to the west, but is located at coordinated 119 km west and 27 km south

Let's add the vectors in each coordinate axis

X axis (East-West)

      -Xvion - Xw = -119

      Xw = -Xavion + 119

      Xw = 119 -108

      Xwi = 1 km

Calculate the speed for time of  t = 0.5 h

     Vwx = Xw / t

     Vwx= 1 /0.5

     Vwx = - 2 km / h

Y Axis (North-South)

    Y plane - Yi = -27

    Y plane = 0

    Yw = 27 km

    Vwy = 27 /0.5

    Vwy = 54 km / h

Let's use the Pythagorean theorem and trigonometry to compose the answer

 Vw = √ (Vwx² + Vwy²)

  Vw = R 2² + 54²

  Vw = 54.04 km / h

  tan θ = Vwy / Vwx

  tan θ = 54/2 = 27

  θ = Tan⁻¹ 1 27

  θ = 87.9º

The speed direction is 87. 9th measure In the third quadrant of the X axis in the direction 90-87.9 = 2.1º  west from the south