A bullet with mass m$=0\mathrm{.}050$ kg and velocity v$\_0=15$ m$/$s imbeds in a block of wood with mass M$=0\mathrm{.}16$ kg$,$ hanging from a rope of length L$=1\mathrm{.}0$ m$.($a$)$ What angle does the rope make with the vertical when the bullet$-$embedded block reaches its maximum height? $($b$)$ How much energy is lost $($if any$)$ in the collision?