So there won\'t be any numbers, I\'m stuck conceptually. In the drawing given, a

Question

So there won't be any numbers, I'm stuck conceptually.
In the drawing given, a boat in (1) is partially submerged in the water (floating).
In the second drawing (drawing (2)), the boat is loaded with a mass.
I'm stuck conceptually for two scenarios.
Scenario 1: Let's say we wanted to calculate the depth of the ship unloaded and loaded, or rather, how far it has submerged for both cases. How would you go about solving that?
Scenario 2: Let's say we just wanted to find the density of either the ship or the fluid. Would we just calculate it regularly with Archimedes principle? Such that the buoyant force is equal to the weight of the fluid displaced, and solve for whichever density were designated to find?
I'm stuck here because I thought that floating is an application of Archimede's principle, where floating requires that the object will displace the amount of fluid equal to its weight, but Archimedes Principle states that the buoyant force is equal to the weight of the fluid displaced. Or are they saying the same thing?

2,

Explanation / Answer

Scenario 1:

Use buoyant force = weight of ship

As this is the only condition so that net force becomes zero and object remains in equilibrium. Using this you can find volume of water displaced which would be equal to volume of ship under water. From there you can calculate the submerged part.

Scenario 2:

Use the same concept

Buoyant force = weight of ship + weight of block

You will get your required results

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