Can you answer this question about water displacement?

Question

Suppose a 10,000,000kg ship has a length of 160m while its breadth is 25m. Estimate how deep the ship sinks assuming the bottom to be rectangular with dimensions 25m by 160m. The ship is in the sea. please answer...

Answer 1

Using Archimedes' Principle, we know that the weight of water displaced by the ship (which is equal to the buoyant force) must be equal to the weight of the ship.

Let the ship sink to a height h m.
So
Weight of water displaced = Weight of the ship
Mass of the ship * g = Volume of water displaced * density of water * g
Cancel out g and substitute the values :
10^7 = (25 * 160 * h) * 1000
h = 2.5 m

If you don't get the correct answer by this, try putting the density of water as 1020 kg/m^3 which is the density of salt water.

Hope this helps.

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Answer 2

The ship has to displace 10^7 kg of water whose volume is 10^7 * 1000/10^6 = 10^4 m^3.
∴ the ship base i.e hull (not the ship itself !) will be in water to a depth = 10^4/(160*25) = 2.5 m.

Answer 3

When an object is floating, it displaces an amount of water equal to its own weight. So your 10 000 000 kg. ship is displacing 10 000 000 kg. of water. In other words, the amount of the ship's hull in the water is equal in volume to 10 000 000 kg. of water.

Now let the depth of immersion be d:
d * 25 * 160 = V
where V = volume of 10 000 000 kg. of water.

We haven't been given the density of the sea water, so we shall have to assume that it is pure -- i.e., 1m3 weighs 1000kg.

I could do the final calculation, but your teacher wouldn't thank me -- and I won't be there when you're doing your GCSEs.