Time it takes for an object to sink? I am trying to determine how long it takes for an object to hit the bottom of the water. I've been looking at Stoke's Law, but can't quite figure out how to get to my answer.
Obviously, there are a lot of variables given, water conditions and which orientation the object travels in the water.
Details:

*

*Object volume: $(8 \times 12 \times 2) \ cm$

*Object weight: $260 \ g$

*Seawater

*Depth: $16 \ m$
 A: The answer is complicated and depends on a variety of different quantities. I can list a couple of forces that you may want to consider:

*

*Drag Force: When a solid object travels through a fluid, it will experience a drag force that resists its motion, given by the formula
$$F_D = \frac{1}{2}C_D A \rho_f v^2$$
where $C_D$ is the drag coefficient (you can look at a table for the drag coefficient of different objects), $A$ is the cross-sectional area, $\rho_f$ is the density of the fluid, and $v$ is the velocity of the object.

Stoke's law here is not valid because the object is not exactly a sphere. However, in high enough speeds, the viscosity of the fluid can matter more.

*

*Buoyant Force: Fluids will exert an upwards force on the object, given by the formula
$$F_B = \rho_f g V$$
where $\rho_f$ is the density of the fluid and $V$ is its volume.

*Weight: The natural downwards attraction of the body to Earth is given as $$F_W = mg.$$
You will then get a differential equation in the form of
$$F_{\text{net}} = m \frac{\text{d}v}{\text{d}t} = F_W - F_D - F_B.$$
From here, you can solve the equation to get the velocity as a function of time, and accordingly how much time it will take for it to travel a certain distance.
