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 257kg?

Question

Quizplus · Accepted Answer

The correct answer is A.The buoyant force on the boat is equal to the weight of the water displaced by the boat. The weight of the water displaced is equal to the density of the water times the volume of the water displaced. The volume of the water displaced is equal to the area of the base of the boat times the depth of the water displaced. The depth of the water displaced is equal to the weight of the boat and the passengers divided by the area of the base of the boat times the density of the water.The weight of the boat and the passengers is:$$W = (200 	ext{ kg}) + (257 	ext{ kg}) = 457 	ext{ kg}$$The area of the base of the boat is:$$A = (1.42 	ext{ m})(4.53 	ext{ m}) = 6.44 	ext{ m}^2$$The depth of the water displaced is:$$d = \frac{W}{Aho} = \frac{457 	ext{ kg}}{(6.44 	ext{ m}^2)(1000 	ext{ kg/m}^3)} = 0.0710 	ext{ m} = 7.10 	ext{ cm}$$

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