In such case the problem gets complicated
So let's tell it's instantaneous, like with a mechanical shock.
When you throw a stone you apply force and in real life it's not an instantaneous process. Simply speaking, it takes some time to throw a stone (it's a short but finite period of time). So you need either to know a time period of force application and cope with it as with impulse or you should say that force is instantaneous and deal with it as with& mechanical shock.
it's like throwing stone by a human, it's all know.... so i hope its enough