Depends on what kind of objects you want to predict. A ball in the air is easy, specially if there is no air friction. Then you can use the math that you learned in high school physics class

the horizonal speed is linear, the vertical speed has an acceleration downward from gravity. Then you use the formulas for that, make a nice equation. You know the height of the floor, so eventually you want the y position to be the same as the height of the floor and then solve for t (time). if you know t you can also calculate the x and z positions.
anyway this is only for an object in a frictionless air, with a flat floor.
But if gets more complex you cannot solve it, but you have to simulate it I guess. A second physics simulation would be a nice idea indeed. It would be easiest if you could clone the current physics world, and then step the clone world until either you are at the time you want to know, or step until some collision happens that you want to know. I don't know how hard it is to clone the current physics world???
If you tell more exact what it is you want (a ball in the air? or just general look ahead in time?) that would be helpfull.