How can you calculate how far the boat sinks into the liquid?

The theory for this is called "Archimedes principle" and as the story goes that dear old Archie shouted "Eureka!", when he was taking a bath and figured it out.

He wrote this down as a law and it goes like this:

"The upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces."

The formula for this is:

Apparentimmersedweight = weight - weight of the displaced liquid.