A $48-$g projectile is fired with a horizontal velocity of $\backslash (477\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and becomes embedded in block $\backslash ($ B $\backslash )$ which has a mass of $3$ kg $.$ After the impact, block $\backslash ($ B $\backslash )$ slides on a $\backslash (30-\backslash$mathrm$\{$kg$\}\backslash )$ carrier $\backslash ($ C $\backslash )$ until it impacts the end of the carrier.

Knowing the impact between $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ is perfectly plastic and the coefficient of kinetic friction between $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ is $0\mathrm{.}2,$ determine the final velocity of the carrier. $($Round the final answer to three decimal places.$)$

The final velocity of the carrier is $\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash$leftarrow $\backslash ).$