Will the water level in a container of water increase, decrease, or stay the same?

Question

I know the answer to this question but I need to know why this happens:

Will the water level in a container of water increase, decrease, or stay the same if you intitially have a couple of rocks in a boat floating on the water then have the rocks moved into the container of water?

The answer: The water level lowers.

BUT WHY?

Answer 1

Because more water is being displaced when the rocks are in the boat.

Answer 2

This can be explained by applying Archimedes' s Principle.

Assuming the boat weighs 1 kg and the rock weighs 1 kg. The water displaced will weigh 2 kg (equal to the buoyant force that keep the boat with the rock inside afloat.)

Now, if we drop the rock into the container, the amount of water displaced comprises 2 part:

- water displaced by the floating empty boat is now 1kg

- water displaced by the submerged rock is less than 1kg (if it were greater than or equal to 1 kg, the rock wouldn't sink to the bottom)

The weight, hence the volume, of displaced water is now less than it was initially. Therefore the water level lowers in the container.

In this explanation, I take the weights of the boat and the rock to be 1 kg each for simplicity. You can substitute them with m kg and n kg and the reasoning is still valid

Answer 3

Think of a really light boat with nothing in it floating above the water.  No displacement.

Add a rock to the mix.  The boat will now displace enough water so that the weight of water displaced is the same as that of the rock.  

The rock is denser than the water so if you now take it out of the boat and dump it in the water then the boat need no longer displace anything.  Since the rock is more dense than the water is the water level rises (as the boat had previously been displacing enough water to compensate for having the rock in it).

Hope that makes sense.