Question

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.

Answer 1

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

Step-by-step 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