The bottom of a flat-bottomed aluminum boat has area = 4.2 m² and mass = 60 kg.If two fishermen and their fishing gear with total mass of 315 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 can be calculated as: 
mass = density x volume
volume = area x depth
mass = density x area x depth
60 kg = (1.0 x 10^3 kg/m^3) x (4.2 m^2) x depth
depth = 0.357 m

When the fishermen and gear are added, the total weight of the boat and contents is:
mass = density x volume
volume = area x depth_f
mass = density x area x depth_f
315 kg + 60 kg = (1.0 x 10^3 kg/m^3) x (4.2 m^2) x depth_f
depth_f = 0.432 m

The difference in depth is:
0.432 m - 0.357 m = 0.075 m

Therefore, the boat will ride 0.075 m lower in the water. The answer is choice C.

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