Solve for v_0 (complex solution)
v_{0}=-\sqrt{R^{2}-v_{f}^{2}}
v_{0}=\sqrt{R^{2}-v_{f}^{2}}\text{, }arg(R)<\pi \text{ or }R=0
Solve for R
R=\sqrt{v_{0}^{2}+v_{f}^{2}}
Solve for v_0
v_{0}=\sqrt{R^{2}-v_{f}^{2}}
v_{0}=-\sqrt{R^{2}-v_{f}^{2}}\text{, }R\geq |v_{f}|
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