Orbital mechanics - falling body

[dreamer_asot]

Hello, my question id the following: when using Tsiolkovsky's equations to determine the velocity of a body after certain period of time, when the engine of a (space)craft is running, life is simple.

But how do you calculate the falling rate of an object that is constantly falling, and then apply that information to find the change of altitude with respect to some change in time?

Let's say the body is already moving with a velocity ai+bj+ck and is at an altitude h (the object is outside Earth's atmosphere). It stops it's engines at time t1 at that altitude h. How does its velocity and altitude change after time delta t, or in other words at time t2?

 

[dreamer_asot]

I think that the problem is not as simple to just account for the Earth's gravitational acceleration, change in h and change in the k component of the velocity vector, that's why I'm asking.