A $5\mathrm{.}50-$g bullet has a muzzle velocity of $250$ m$/$s when fired by a rifle with a weight of $30\mathrm{.}0$ N$.$

$($a$)$ Determine the recoil speed of the rifle.

$\mathrm{.}449$ m$/$s

$($b$)$ If a marksman with a weight of $625$ N holds the rifle firmly against his shoulder, determine the recoil speed of the shooter and rifle.

$\mathrm{.}0206$ m$/$s