A $5\mathrm{.}50$ g bullet moving at $979\frac{m}{s}$ strikes a $800$ g wooden block at rest on a frictionless surface. The bullet emerges, traveling in the same direction with its speed reduced to $462\frac{m}{s}.($a$)$ What is the resulting speed of the block? $($b$)$ What is the speed of the bullet$-$block center of mass?

$($a$)$ Number $$ Units

$($b$)$ Number $$ Units