$(50$pts$)$ The $5$ oz$.$ ball is translating with velocity vA $=80$ ft$/$s perpendicular to the bat just before the impact. The player is swinging the $31$ oz$.$ bat with angular velocity $=6$ rad$/$s before the impact. Point C is the bat$$s instantaneous center both before and after the impact. The distances b $=14$ in and $=26$ in$.$ The bat$$s moment of inertia about its cent of mass is IB $=0\mathrm{.}033$ slug$-$ft$2.$ The coefficient of restitution is e $=0\mathrm{.}6,$ and the duration of the impact is $0\mathrm{.}008$ s$.$ Determine the magnitude of the velocity of the ball after the impact and the average force Ax exerted on the bat by the player during the impact if d $=8$ in$.$