Launching an Ideal Rocket--Is This Correct?

I am in a hole 13 m deep and launch a rocket vertically upwards. While the engines are on, the rocket acclerates upwards at a constant 6.0 m/s². After 3.0 s the fuel runs out and the rocket enters free-fall. Ideal rocket assumptions: mass of the rocket is constant, air resistance is negligible, the rotation of the earth has no effect, the rocket is always near the earth so g is constant.

Questions

1. What is the maximum height of the rocket? Determine this analytically to check with the simulation. Begin
2. At what time does the rocket hit the ground?

Problem © 2003 Vern Lindberg using Wolfgang Christian's Physlets.