Hermione Granger uses her Time-Turner and is suddenly whisked away to a cold April night in 1912 in the middle of the Atlantic ocean. She is on the Titanic enjoying the party. In the distance she sees a large white object approaching the ship. She thinks its pretty and not much danger to the ship so she carries on with her festivities. Later the large white object (an iceberg) hits the ship, and the ship begins to sink. As the ship is sinking she thinks, hm, it wasnt that big of an ice-berg (and of course this ship cant sink ...). What percentage of the iceberg was under water? Let the density of the water be 1.0 g/cm3, and the density of the ice be 0.92 g/cm3. Express your answer as a percentage (not a decimal).

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Senior

Mathematics

11 June, 01:54

Hermione Granger uses her Time-Turner and is suddenly whisked away to a cold April night in 1912 in the middle of the Atlantic ocean. She is on the Titanic enjoying the party. In the distance she sees a large white object approaching the ship. She thinks its pretty and not much danger to the ship so she carries on with her festivities. Later the large white object (an iceberg) hits the ship, and the ship begins to sink. As the ship is sinking she thinks, hm, it wasnt that big of an ice-berg (and of course this ship cant sink ...). What percentage of the iceberg was under water? Let the density of the water be 1.0 g/cm3, and the density of the ice be 0.92 g/cm3. Express your answer as a percentage (not a decimal).

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Answers (1)

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Leanna Dennis · Answer 1

The percentage of ice berg under water is 92%

Step-by-step explanation:

From Archimede's Principle, we know that the Buoyant Force is equal to the weight of fluid displaced. Hence, the mass of fluid (water) displaced, will be equal to the weight of the object in vacuum.

Therefore,

(Density of Water) (Volume of Ice Berg inside Water) = (Density of Ice Berg) (Total Volume of Ice Berg)

(Volume of Ice Berg inside Water) / (Total Volume of Ice Berg) = (Density of Ice Berg) / (Density of water)

(Volume of Ice Berg inside Water) / (Total Volume of Ice Berg) = % of Ice Berg Under Water = (0.92 g/cm³) / (1.0 g/cm³) * 100%

% of Ice Berg Under Water = 92%