Answer:
[tex]\large \boxed{R_{\text{m}} = 5R_{\text{e}}}[/tex]
Explanation:
A projectile has its maximum range when you fire it at an angle of 45°.
The formula becomes
[tex]R = \dfrac{v^{2}}{g}[/tex]
If you are comparing the ranges on the Moon and the Earth,
[tex]\dfrac{R_{\text{m}}}{R_{\text{e}}} = \dfrac{v^{2}}{g_{\text{m}}}\div \dfrac{v^{2}}{g_{\text{e}}} = \dfrac{v^{2}}{g_{\text{m}}}\times \dfrac{g_{e}}{{v^{2}}} = \dfrac{ g_{\text{e}}}{g_{\text{m}}}\= \dfrac{g}{0.2g} = \textbf{5}\\\\\large \boxed{\mathbf{R_{\text{m}} = 5R_{\text{e}}}}[/tex]
