A 200.0 kg flat-bottomed boat floats in fresh water,which has a density of 1000.0 kg/m³.Assuming that the base of the boat is 1.42 m wide and 4.53 m long,how much of the boat is submerged when it carries three passengers whose total mass is 193 kg?

Question

Quizplus · Accepted Answer

The correct answer is A.The volume of the boat that is submerged is equal to the volume of water that is displaced by the boat. The volume of water that is displaced is equal to the mass of the boat and the passengers divided by the density of water. The mass of the boat and the passengers is 200.0 kg + 193 kg = 393 kg. The density of water is 1000.0 kg/m^3. Therefore, the volume of water that is displaced is 393 kg / 1000.0 kg/m^3 = 0.393 m^3. The base of the boat is 1.42 m wide and 4.53 m long. Therefore, the area of the base of the boat is 1.42 m * 4.53 m = 6.44 m^2. The height of the boat that is submerged is equal to the volume of water that is displaced divided by the area of the base of the boat. Therefore, the height of the boat that is submerged is 0.393 m^3 / 6.44 m^2 = 0.0611 m = 6.11 cm.

A 2000 Kg Flat-Bottomed Boat Floats in Fresh Water,which Has a a Density