$1.)$ A $30\mathrm{.}0$ g bullet moving at $400.$ m$/$s strikes a ballistic pendulum of mass $2\mathrm{.}50$ kg$.$ The bullet emerges with a speed of $100.$ m$/$s$.($a$)$ To what height does the pendulum rise?$($b$)$ How much work was done by the bullet passing through the pendulum? $($Assume an inelastic collision$)$