A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is:

For maximum range of projectile, $\mathrm{\theta } \mathrm{should} \mathrm{be} {45}^0.$

$\mathrm{R} = \frac{{\mathrm{u}}^2\sin 2\mathrm{\theta }}{\mathrm{g}} = \frac{{\mathrm{u}}^2\sin \left(2 \times {45}^0\right)}{\mathrm{g}}$

$\Rightarrow {\mathrm{R}}_{\max } = \frac{{\mathrm{u}}^2}{\mathrm{g}}$

Given, u = 20 ${\mathrm{ms}}^{-1}$ and g = $10 {\mathrm{ms}}^{-2}$

${\mathrm{R}}_{\max } = \frac{{\left(20\right)}^2}{10} = 40 \mathrm{m}$