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Agent Arlene devised the following method of measuring the muzzle velocity of a rifle. She fires a bullet into a $4\mathrm{.}200-kg$ wooden block resting on a smooth surface, and attached to a spring of spring constant $k=138\mathrm{.}0\frac{N}{m}.$ The bullet, whose mass is $7\mathrm{.}750$ 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 $1)$

Figure

$1$ of $1$

Part A

What is the speed $v$ of the bullet?

Express your answer using four significant figures.

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