The bottom of a flat-bottomed aluminum boat has an area of 4.0 m², and the boat's mass is 120 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.0 * 10³kg/m³)

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Quizplus · Accepted Answer

The buoyant force equals the weight of the boat. Using Archimedes' principle: ρ_water * g * V_displaced = m_boat * g. Solving for V_displaced (volume of water displaced) gives V_displaced = m_boat / ρ_water. Substituting the given values: V_displaced = 120 kg / 1000 kg/m³ = 0.12 m³. Since V_displaced = area * depth, depth = 0.12 m³ / 4.0 m² = 0.030 m.

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