$4)$ A $\backslash (5\mathrm{.}00-\backslash$mathrm$\{$g$\}\backslash )$ bullet moving with an initial speed of $\backslash (400\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ is fired into and passes through a $\backslash (1\mathrm{.}00-\backslash$mathrm$\{$kg$\}\backslash )$ block, as shown in the Figure. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring of force constant $\backslash (900\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ If the block moves $5\mathrm{.}00$ cm to the right after impact, find

$($a$)$ the speed at which the bullet emerges from the block

$($b$)$ the energy lost in the collision.

Assume for an approximation that the block very quickly reaches its maximum velocity $($Vi$),$ keeps the same mass, and the bullet kept going with a constant velocity, $\backslash ($ v $\backslash ).$