$\begin{array}{l}
S = \frac{{{v^2}}}{{2\mu g}} = \frac{{v_0^2 + 2gh}}{{2\mu g}}\\
 = \frac{{v_0^2}}{{2\mu g}} + \frac{{2gh}}{{2\mu g}} = \frac{h}{\mu } + \frac{{v_0^2}}{{2\mu g}}
\end{array}$