$0\mathrm{.}0250-$kg bullet is accelerated from rest to a speed of $550$ m$/$s in a $3\mathrm{.}00-$kg rifle. The pain of the rifle's kick is much worse if you hold the gun loosely a few centimeters from your shoulder rather than holding it tightly against your shoulder. $($a$)$ Calculate the recoil velocity of the rifle if it is held loosely away from the shoulder. $($b$)$ How much kinetic energy does the rifle gain? $($c$)$ What is the recoil velocity if the rifle is held tightly against the shoulder, making the effective mass $28\mathrm{.}0$ kg$?($d$)$ How much kinetic energy is transferred to the rifle$-$shoulder combination? $($e$)$ Calculate the momentum of a $110-$kg football player running at $8\mathrm{.}00$ m$/$s$.$ Compare the player's momentum with the momentum of a hard$-$thrown $0\mathrm{.}410-$kg football that has a speed of $25\mathrm{.}0$ m$/$s$.$ Discuss its relationship to this problem