The bottom of a flat-bottomed aluminum boat has area = 4.10 m² and mass = 65.0 kg.If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat,how much lower will the boat ride in the water? (H₂O density = 1.0 × 10³ kg/m³)

Question

Quizplus · Accepted Answer

The weight of the boat filled with water (displaced water) is equal to the weight of the boat and its contents. We can use the formula:

(displaced water volume) x (water density) x (gravity) = (boat + contents mass) x (gravity)

Rearranging the formula to solve for the displaced water volume:

displaced water volume = (boat + contents mass) x (gravity) / (water density x gravity)

displaced water volume = (305 kg + 65 kg) / (1000 kg/m^3)

displaced water volume = 0.37 m^3

Since the boat has a flat bottom, the displaced water volume is equal to the volume of water directly under the boat. Therefore, the depth that the boat rides lower in the water is:

depth = displaced water volume / (boat bottom area)

depth = 0.37 m^3 / (4.10 m^2)

depth = 0.0902 m

So the boat rides 0.0902 m lower in the water with the fishermen and their gear on board. The correct answer is C.

The Bottom of a Flat-Bottomed Aluminum Boat Has Area =