\left\{ \begin{array} { l } { v _ { 0 } t _ { 1 } = 3 } \\ { 1 - 1 - 2 = \frac { 1 } { 2 } g t _ { 1 } ^ { 2 } } \\ { v _ { 0 } t _ { 2 } = 12 } \\ { H = \frac { 1 } { 2 } g t _ { 2 } ^ { 2 } } \end{array} \right.
Solve for v_0, t_1, g, t_2, H (complex solution)
v_{0}=-\frac{3i\sqrt{g}}{2}\text{, }t_{1}=2ig^{-\frac{1}{2}}\text{, }g\neq 0\text{, }t_{2}=8ig^{-\frac{1}{2}}\text{, }H=-32
v_{0}=\frac{3i\sqrt{g}}{2}\text{, }t_{1}=-2ig^{-\frac{1}{2}}\text{, }g\neq 0\text{, }t_{2}=-8ig^{-\frac{1}{2}}\text{, }H=-32
Solve for v_0, t_1, g, t_2, H
v_{0}=-\frac{3\sqrt{-g}}{2}\text{, }t_{1}=-2\sqrt{-\frac{1}{g}}\text{, }g<0\text{, }t_{2}=-8\sqrt{-\frac{1}{g}}\text{, }H=-32
v_{0}=\frac{3\sqrt{-g}}{2}\text{, }t_{1}=2\sqrt{-\frac{1}{g}}\text{, }g<0\text{, }t_{2}=8\sqrt{-\frac{1}{g}}\text{, }H=-32
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