Let us consider a projectile launched, so that its initial velocity u makes an angle q with the horizontal. In the following diagram, horizontal direction is taken as X-axis and vertical direction is taken as the Y-axis.
\(\tt u = u_{x}\widehat{i}+ u_{y}\widehat{j} \)\(\tt u = u cos \theta \widehat{i}+ u sin\theta \widehat{j} \)
It can be seen that the X-axis is parallel to the horizontal, Y-axis is parallel to the vertical and u lies in the XY-plane. The constant acceleration a is given as
\(\tt a = a_{x}\widehat{i}+ a_{y}\widehat{j} \)
where, \(\tt a_{x}\) = 0 (Since, there is no acceleration along X-axis)
\(\tt a_{y}\) = -g (Since, the acceleration is downwards and equal to g)
Velocity after time t can be given as
\(\tt v_{t} = vcos \theta \widehat{i} (u sin \theta -gt)\widehat{j}\)