Solution to 2008 Problem 10

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.

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