Answer
$14.43$ revolutions
Work Step by Step
Lets convert the horizontal distance to meters:
$1ft\approx 0.3048m\Rightarrow 60ft=0.3048\times 60\approx 18.288m $
Lets convert the speed to $\frac{m}{s}$:
$1mile=1609m;1hr=3600s\Rightarrow 85\dfrac {mi}{h}=85\times \dfrac {1609m}{3600s}\approx 38\dfrac {m}{s}=v_{0}$
Time passed until the baseball reaches the home plate is:
$t=\dfrac {d}{v_{0}}=\dfrac {18.288m}{38\dfrac {m}{s}}\approx 0.48s$
Spin of the baseball is:
$w=1800\dfrac {rev}{\min }=1800\dfrac {rev}{60sec}=30\dfrac {rev}{s}$
So the total revolutions will be:
$N=wt=30\dfrac {rev}{s}\times 0.48s=14.43$
