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 :
$$\eqalign{ & \hat u = \hat i + 2\hat j = {u_x}\hat i + {u_y}\hat j \cr & \Rightarrow u\,\cos \theta = 1,\,\,\,\,u\,\sin \theta = 2 \cr & y = x\,\tan \theta - \frac{1}{2}\frac{{g{x^2}}}{{u_x^2}} \cr & \therefore y = 2x - \frac{1}{2}g{x^2} = 2x - 5{x^2} \cr} $$