State Space / Ball Trajectory Question

Hi All,

How do you think it will convert the following equations:

(dx^2/dt^2) = - k.((dx/dt)^2)

and

(dy^2/dt^2)= - g - k.((dy/dt)^2)

Taking into consideration I need to calculate the x,y,xDot, and yDot for
each state only using the values known for the previous state

so that I have make the matrix A for the equation

P(t+1) = A P(t)


where P is column vector containing (x,y,xDot,yDot), and I want to predict
P(t+1) from the P(t) I have. This is for part of a kalman filter, which I
have set up, to predict the trajectory of a ball.

I have been looking into this problem for a long time, and I know there must
be a solution to this, but still not been able to get there. I has been
mentioned that I need to use state space representation??? Then Runge-Kutta

Adam