Agent Arlene devised the following method of measuring the muzzle velocity of a rifle. She fires a bullet into a $\backslash (4\mathrm{.}700-\backslash$mathrm$\{$kg$\}\backslash )$ wooden block resting on a smooth surface, and attached to a spring of spring constant $\backslash ($ k$=136\mathrm{.}0\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The bullet, whose mass is $7\mathrm{.}900$ g $,$ remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be $9\mathrm{.}460$ cm $.($Figure $1)$

What is the speed $\backslash ($ v $\backslash )$ of the bullet?

Express your answer using four significan