#### Answer

The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$

#### Work Step by Step

We can find $f$, the fraction of the earth's circumference that the plane flies:
$f = \frac{5000~mi}{2\pi ~4000~mi}$
$f = 0.199$
We can find the angle in degrees that the plane flies with respect to the earth's surface:
$\theta = (0.199)(360^{\circ})$
$\theta = 71.64^{\circ}$
We can find the plane's angular velocity with respect to the earth's surface:
$\omega = \frac{\Delta \theta}{\Delta t}$
$\omega = \frac{71.64^{\circ}}{9.0~h}$
$\omega = 7.96^{\circ}/h$
The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$.