The energy stored in a spring compressed a distance $s$ from its equilibrium position is

$\begin{align*}\frac{1}{2}k s^2\end{align*}$
This must equal $m v^2/2$ in order for the ball to travel with velocity $v$ after it is released. Therefore,
$\begin{align*}\boxed{s = v\sqrt{\frac{m}{k}}}\end{align*}$
Therefore, answer (B) is correct.

Solution to 2008 Problem 10