Hukum Kekekalan Energi Mekanik

\begin{equation*}
\begin{split}
EM_1 & = EM_2 \\\\
EP_1 + EK_1 & = EP_2 + EK_2 \\\\
m \:.\: g \:.\: h_1 + \tfrac{1}{2} \:.\: m \:.\: v_1^2 & = EP_2 + EK_2 \\\\
0 + \tfrac{1}{2} \:.\: 1 \:.\: 30^2 & = EP_2 + EK_2 \\\\
450 & = EP_2 + EK_2 \\\\
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
&  EP_2 : EK_2 = 3 : 2 \\\\
&  EP_2 = \tfrac{3}{5} \times 450 = 270 \text{ J} \\\\
& EK_2 = \tfrac{2}{5} \times 450 = 180 \text{ J}
\end{split}
\end{equation*}

Tinggi benda

\begin{equation*}
\begin{split}
EP_2 & = m \:.\: g \:.\: h_2 \\\\
540 & = 1 \:.\: 10 \:.\: h_2 \\\\
h_2 & = 54 \text{ m}
\end{split}
\end{equation*}

Kecepatan benda

\begin{equation*}
\begin{split}
E_{k2} & = \tfrac{1}{2} \:.\: m \:.\: v_1^2 \\\\
360 & = \tfrac{1}{2} \:.\: 1 \:.\: v_1^2 \\\\
v_2^2 & = 720 \\\\
v_2 & = 12 \sqrt{5} \text{ m/s}
\end{split}
\end{equation*}