A $1-$kg blue ball with an initial linear velocity v$0=100$ m$/$s is flying toward a pendulum. If the coefficient of restitution e between the ball and the pendulum is $0\mathrm{.}7,$ determine i$)$ linear velocity of the ball right after impact, ii$)$ linear velocity of the sphere right after impact, and iii$)$ angular velocity of the pendulum right after impact, knowing Mass of the slender rod $=22$ kg$,$ mass of the green sphere $=40$kg$,$ and length of the slender rod L $=500$ mm$.$