A $0\mathrm{.}792$ kg ball drops vertically onto a floor, hitting with a speed of $31\mathrm{.}5$ m$/$s$.$ It rebounds with an initial speed of $13\mathrm{.}0$ m$/$s$.($a$)$ What impulse acts on the ball during the contact? $($b$)$ If the ball is in contact with the floor for $0\mathrm{.}0321$ s$,$ what is the magnitude of the average force on the floor from the ball?