A $8\mathrm{.}69-$g bullet is moving horizontally with a velocity of $+354$ m$/$s$,$ where the sign $+$ indicates that it is moving to the right $($see part a of the drawing$).$ The bullet is approaching two blocks resting on a horizontal frictionless surface. Air resistance is negligible. The bullet passes completely through the first block $($an inelastic collision$)$ and embeds itself in the second one, as indicated in part b$.$ Note that both blocks are moving after the collision with the bullet. The mass of the first block is $1231$ g$,$ and its velocity is $+0\mathrm{.}689$ m$/$s after the bullet passes through it$.$ The mass of the second block is $1648$ g$.($a$)$ What is the velocity of the second block after the bullet imbeds itself? $($b$)$ Find the ratio of the total kinetic energy after the collision to that before the collision.