how much high(about physic and mathematics)?

If we shoot a spherical object like a rock, into the mud,and the mud is lame enough, some part of the rock sinks into the mud. A young physicist throws a stone from a certain height to be plunged into the mud.

Yet if Stone wants to double the amount before the case goes down into the mud, how high should it start?

Explain your answer.(the answer is not 2)