A 200-kg flat-bottomed boat floats in fresh water,which has a density of 1000 kg/m³.If the base of the boat is 1.42 m wide and 4.53 m long,to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is $257 \mathrm {~kg} \text { ? }$ A)7.10 cm B)7.53 cm C)7.95 cm D)8.52 cm

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Quizplus · Accepted Answer

The correct answer is A.The total mass of the boat and passengers is 200 kg + 257 kg = 457 kg. The volume of water displaced by the boat is equal to the mass of the boat and passengers divided by the density of water, which is 457 kg / 1000 kg/m3 = 0.457 m3. The area of the base of the boat is 1.42 m * 4.53 m = 6.44 m2. The depth to which the bottom of the boat is submerged is equal to the volume of water displaced divided by the area of the base of the boat, which is 0.457 m3 / 6.44 m2 = 0.071 m = 7.10 cm.

A 200-Kg Flat-Bottomed Boat Floats in Fresh Water,which Has a Density