Physics - Kinematics Question with Solution | TestHub

$\mathrm{y}=2\mathrm{x}-9{\mathrm{x}}^2$
Comparing above equation with general equation of trajectory of projectile$y=x\tan \mathrm{\theta }\left(1-\frac{x}{R}\right)$
$\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{ }\mathrm{\theta }=2$
$\Rightarrow \mathrm{s}\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{\theta }=\frac{2}{\sqrt{5}}$or$\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{ }\mathrm{\theta }=\frac{1}{\sqrt{5}}$
$\mathrm{\theta }={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{2}{\sqrt{5}}\right)$or$\mathrm{\theta }={\mathrm{c}\mathrm{o}\mathrm{s}}^{-1}\left(\frac{1}{\sqrt{5}}\right)$
And R = 2/9
$\mathrm{R}=\frac{{v_0}^2\sin 2\mathrm{\theta }}{\mathrm{g}}=\frac{2}{9}$
After substituting the value for g and sin 2θ. We get$v_0=\frac{3}{5}$m/s