Grasshopper can hover for a while because, at least at that stage in its flight, it is heavier than the returning F9 core. As it burns more and more fuel it becomes lighter and lighter, and I believe that towards the end of Grasshopper flights it is too light to hover.
The landing that Grasshopper has been doing recently, and which the F9 core will do, has been termed a "hover-slam" by SpaceX. Basically it decelerates rapidly, hitting 0m/s right when it also hits the ground. If it did not cut out the engine right at that point, it would begin going back up (until the fuel ran out).
The landing that Grasshopper has been doing recently, and which the F9 core will do, has been termed a "hover-slam" by SpaceX. Basically it decelerates rapidly, hitting 0m/s right when it also hits the ground. If it did not cut out the engine right at that point, it would begin going back up (until the fuel ran out).