Launching an Ideal Rocket

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.

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. As usual, holding the mouse button down will display coordinates of the cursor. For the animation this is in meters, for the graph refer to the axis labels.

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.