Projectile motion: acceleration  a=-g is a constant in the vertical (y)direction.
It means that Vy(t)=Vy(t=0)+a*t =Vy(t=0)-g*t
The average speed from 0 to t is equal to
(V(t=0)+V(t))/2= V(t=0)+a*t/2= V(t=0)-g*t/2
because velocity change linearly.

So the distance traveled in y direction= average speed * t = V(t=0)*t - gt[sup]2[/sup]/2
The distance traveled in x direction is Vx*t because velocity did not change in the horizontal direction.

This applet let you play with projectile.
You can adjust the initial (x,y) position of particle with mouse.
Drag the red arrow to change the initial velocity.
You can also change the above parameters with slider (x,y,vx,vy).
Equation for projectile motion with your initial conditions are displayed.
Click Initialize to reset time to zero and adjust new initial condition.
The simulation will remember the last three traces.

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