I have taken up Applied Maths as a Leaving Cert subject, One of the chapters I am studying is "Projectiles in Motion", this I realised is quite similar to calculating a rockets trajectory.
The difference is that, the applied maths equations for motion, do not take into account variables that can dramatically change a flights, flight path. Air Resistance ie Drag can slow down an object by a tremendous amount, thus dramatically changing the flights course.
Velocity Values, In the Equations of Motion the initial velocity is a fixed figure for velocity. This figure increments downwards every 1 second. Until we get Vj=0 at apogee. In reality the rockets velocity may increase 5 seconds into the flight. Due to differences in rocket motor construction.
Learning all this, I realised it would be simply unrealistic to assume I could take into consideration all these independent variables while doing calculations by hand. Computers are great due to the fact that they can do incredibly fast calculations, and can do anything you program it to do.