The simplest approach would be using Stokes law for settling velocity. This equation will tell you how fast a sphere with a certain radius and density will sink in a fluid which has it’s own density and viscosity.
V=2/9(gr2)(d1-d2)/µ
where
V = velocity of fall (cm/sec)
g = acceleration of gravity (cm/sec2)
r = “equivalent” radius of particle
d1 = density of particle (g/cm3)
d2 = density of medium (g/cm3)
µ = viscosity of medium (g/cm-sec)
If you’ve ever been in the water you might have noticed that things tend to fall much slower than in air. But more weirdly is that they don’t seem to speed up! This is because the terminal velocity of objects in water is typically reached rather quickly.
For the second part of your question the weight of an object doesn’t matter as much as its density. A rock will fall but a battleship will float. In a way you might think of objects that float in water as having a negative terminal velocity, they want to rise.
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