Answer
a) $104{}^\circ $
b) Decreases
Work Step by Step
a)
Let the velocity of the plane with respect to ground be ${{\mathbf{v}}_{1}}$.
The velocity of the plane with respect to wind is ${{\mathbf{v}}_{2}}$.
The velocity of wind with respect to earth is $\mathbf{u}$.
The angle of the plane with respect to wind is
$\begin{align}
& \tan \theta =\frac{{{\mathbf{v}}_{1}}}{\mathbf{u}} \\
& \tan \theta =\frac{310}{75} \\
& \theta =76{}^\circ
\end{align}$
Here, $\theta $ is the angle of the plane’s velocity with respect to the wind.
So, the direction of the plane from the east to north at an angle $\left( \gamma \right)$ is
$\begin{align}
& \gamma =180{}^\circ -76{}^\circ \\
& =104{}^\circ
\end{align}$
Hence, the direction for where you should head the plane is $104{}^\circ $ from east to north.
(b)
The angle of the plane with respect to wind is
$\tan \theta =\frac{{{\mathbf{v}}_{1}}}{\mathbf{u}}$
When the airspeed increases, then the value of $\tan \theta $ decreases; the value of $\theta $ also decreases. Maintaining the angle also increases the plane’s speed with respect to the earth.
Hence, the direction angle decreases.
