A projectile is given an initial velocity of $$\left( {\hat i + 2\hat j} \right)m/s$$    where $${\hat i}$$ is along the ground and $${\hat j}$$ is along the vertical. If $$g = 10\,m/{s^2},$$   the equation of its trajectory is :

Solution :
From equation, $$\vec v = \hat i + 2\hat j$$
$$\eqalign{ & \Rightarrow x = t\,......\left( {\text{i}} \right) \cr & y = 2t - \frac{1}{2}\left( {10{t^2}} \right)\,......\left( {{\text{ii}}} \right) \cr} $$
From (i) and (ii),
$$y = 2x - 5{x^2}$$