Explanation

(b) Given, $\overrightarrow{\mathbf{u}} = \widehat{\mathbf{i}} + 2\widehat{\mathbf{j}} = u_{x}\widehat{\mathbf{i}} + u_{y}\widehat{j}$
Then $u_{x} = u\cos\theta$
and $u_{y} = 2 = \ u\cos\theta$
$\therefore\ \tan{\theta = \frac{u\sin\theta}{u\cos\theta}} = \frac{2}{1} = 2$
The equation of trajectory of a projectile motion is
$y = x\tan\theta - \frac{gx^{2}}{2u^{2}\cos^{2}\theta}$
$= \ x\tan\theta - \frac{gx^{2}}{2\left( u\cos\theta \right)^{2}}$
$= x \times 2 - \frac{10 \times x^{2}}{2(1)^{2}} = 2x - 5x^{2}$