Aboat has a mass of 20 kg and will carry 110 kg of passengers across a pool. if 50% of the boat is submerged, what is the total volume of the boat?

0.26 m³

Explanation:

There are three forces on the boat: weight of the boat, weight of the passengers, and buoyancy.

∑F = ma

B - mg - Mg = 0

Buoyant force is equal to the weight of the fluid displaced.

ρVg - mg - Mg = 0

ρV - m - M = 0

V = (m + M) / ρ

Given m = 20 kg, M = 110 kg, and ρ = 1000 kg/m³:

V = (20 + 110) / 1000

V = 0.13 m³

Since this is half of the boat's volume, the total volume is 0.26 m³.

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

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