Question

An airplane is flying east at 90km/h and encounters a wind from the north at 40km/h your task is to determine the resulting ground speed of the airplane which should include both speed and directions

Answer 1

Given,

The initial eastward velocity of the airplane. v₁=90 km/hr

The speed of the wind from the north, v₂=40 km/hr

In vector notation, the velocity of the airplane is

`\vec{v_1}=90\hat{i}`

And the velocity of the wind in vector notation is

`\vec{v_2}=-40\hat{j}`

Thus the resultant velocity is,

`\begin{gathered} \vec{V}=\vec{v_1}+\vec{v_2} \\ =90\hat{i}-40\hat{j} \end{gathered}`

The magnitude of this velocity, i.e., resulting speed of the airplane is

`\begin{gathered} V=\sqrt[]{90^2+40^2} \\ =98.5\text{ km/hr} \end{gathered}`

The direction of the resulting velocity of the airplane is,

`\begin{gathered} \theta=\tan ^(-1)((-40)/(90)) \\ =-24^(\circ) \end{gathered}`

The negative sign in the angle is given in the clockwise direction from the positive x-axis.

Thus the speed of the plane is 98.5 km/hr and the direction is -24°