Answer
The ball makes 30 revolutions.
Work Step by Step
We can find the time it takes to reach maximum height:
$t = \frac{v_{y0}}{g}$
$t = \frac{v_0~sin~\theta}{g}$
$t = \frac{(60~m/s)~sin~20^{\circ}}{9.8~m/s^2}$
$t = 2.094~s$
We can find the number of revolutions:
$\theta = (90~rad/s)(2.094~s)$
$\theta = 188.46~rad$
$\theta = (188.46~rad)(\frac{1~rev}{2\pi~rad})$
$\theta = 30~rev$
The ball makes 30 revolutions.
