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 $257 \mathrm {~kg} ?$

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 boat submerged.The area of the base of the boat is:$$A = 1.42 \mathrm{~m} 	imes 4.53 \mathrm{~m} = 6.44 \mathrm{~m^2}$$The weight of the boat and passengers is:$$W = (200 \mathrm{~kg} + 257 \mathrm{~kg}) 	imes 9.81 \mathrm{~m/s^2} = 4470 \mathrm{~N}$$The buoyant force on the boat is:$$F_b = ho g V = 1000 \mathrm{~kg/m^3} 	imes 9.81 \mathrm{~m/s^2} 	imes A 	imes d$$Setting the buoyant force equal to the weight of the boat and passengers, we get:$$1000 \mathrm{~kg/m^3} 	imes 9.81 \mathrm{~m/s^2} 	imes 6.44 \mathrm{~m^2} 	imes d = 4470 \mathrm{~N}$$Solving for d, we get:$$d = 0.071 \mathrm{~m} = 7.10 \mathrm{~cm}$$

A 200-Kg Flat-Bottomed Boat Floats in Fresh Water, Which Has 257 kg?257 \mathrm {~kg} ?257 kg?

A 200-Kg Flat-Bottomed Boat Floats in Fresh Water, Which Has $257 \mathrm {~kg} ?$