$[16$ pts$]$ A $12\mathrm{.}5$ cm radius wheel pitching machine starts from rest, spinning a ball at the bottom of a vertical circular path at a constant angular acceleration. The ball will exit the machine after $2\mathrm{.}1$ revolutions. Use $g=9\mathrm{.}8\frac{m}{s^2}.[$Answer in $3$ significant figures$]$

a$)[4$ pts$]$ If the ball exits with an angular speed of $1370$ rpm $,$ what is the angular acceleration of the machine?

b$)[4$ pts$]$ How much time does it take the machine to spin the ball up to the final speed?

c$)[4$ pts$]$ Once the ball leaves the machine at a height $1\mathrm{.}0$ m above ground, it becomes a projectile motion. How high $($h$)$ will the ball reach?

d$)[4$ pts$]$ How far will the ball land on the ground $(x_f)$ from the point it leaves the machine?