A gymnast doing a front flip received an average torque of $523$ Nm during the $0\mathrm{.}31$ seconds during the

takeoff phase $($i$.$e$.,$ the time during which the feet push on the ground$).$ If the gymnast started the flip from a

stationary position, calculate $($a$)$ the angular impulse exerted on the gymnast during the takeoff phase, and $($b$)$

the gymnast$$s angular velocity immediately after the takeoff phase if her moment of inertia is $5$ kg$*$m$2$