Newtonian Mechanics

This is a question about newtonian mechanincs.
Thanks for your time.The solutions are not easy and anybody that knows where i can find the answer please writes me
Please use the 2 dimensions as shown, no need for a third one
Gravity _ particles
we have a particle that is moving along the axe x, then we have the gravity force that is not on the axe x but the center of the gravity (the center of the massive object) and has a distance h from the axe x.
In time t what will be the distance that the object will travel?
What are the equations of velocity,displacement with time?
We need the r and h according to time.If i have the equation then i can put different h and r and see the result. Its really important the time, is given.
In a few words, with given time what can be the maximum distance that the particle can be , knowing that the particle will fall on this object and has the given time to do that.
Particle
*---->-------------------------->x
| Uin (initial Velocity)
|
|
|
|
|
h
|
|
|------------r-----------------* Massive star
_y________________________________________________ ___

thanks for your time