$v_{\min }=v_{0} \sqrt{\frac{1-\mu_{s} \frac{R g}{v_{0}^{2}}}{1+\mu_{s} \frac{v_{0}^{2}}{R g}}}, \quad v_{\max }=v_{0} \sqrt{\frac{1+\mu_{s} \frac{R g}{v_{0}^{2}}}{1-\mu_{s} \frac{v_{0}^{2}}{R g}}}$

$v_{\min }=v_{0} \sqrt{\frac{1}{1+\mu_{s} \frac{v_{0}^{2}}{R g}}}, \quad v_{\max }=v_{0} \sqrt{\frac{\mu_{s}+\frac{R g}{v_{0}^{2}}}{1-\frac{v_{0}^{2}}{R g}}}$

$v_{\min }=v_{0} \sqrt{\frac{\mu_{s}-\frac{R g}{v_{0}^{2}}}{1+\mu_{s}}}, \quad v_{\max }=v_{0} \sqrt{\frac{1+\mu_{s}}{\mu_{s}-\frac{v_{0}^{2}}{R g}}}$

$v_{\min }=v_{0} \sqrt{\frac{1-\mu_{s} \frac{v_{0}^{2}}{R g}}{1+\mu_{s} \frac{R g}{v_{0}^{2}}}}, \quad v_{\max }=v_{0} \sqrt{\frac{1+\mu_{s} \frac{v_{0}^{2}}{R g}}{1-\mu_{s} \frac{R g}{v_{0}^{2}}}}$