1. A buoyant force of 790 N lifts a 214 kg sinking boat. What is the boat's
net acceleration?

The boat's  net acceleration is -6.12 m/s²

Given that:

Buoyant force = 790 N, mass (m) = 214 kg, acceleration due to gravity (g) = 9.81 m/s²

Net force = Buoyant force - mg = 790 - (214 * 9.81) = -1309.34 N

Net acceleration = Net force / mass

Net acceleration = -1309.34 N / 214 kg = -6.12 m/s²

The boat's  net acceleration is -6.12 m/s²

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The net acceleration of the boat is approximately 6.12 m/s² downwards

Explanation:

The buoyant or lifting force applied to the boat = 790 N

The mass of the boat lifted by the buoyant force = 214 kg

The force applied to a body is defined as the product of the mass and the acceleration of the body. Therefore, the buoyant force, F, acting on the boat can be presented as follows;

Fₐ = F - W

The weight of the boat = 214 × 9.81 = 2099.34 N

Therefore;

Fₐ = 790 - 2099.34  = -1309.34 N

Fₐ = Mass of the boat × The acceleration of the boat

Given that the buoyant force, Fₐ, is the net force acting on the boat, we have;

F = Mass of the boat × The net acceleration of the boat

F = -1309.34 N =  214 kg × The net acceleration of the boat

∴ The net acceleration of the boat = -1309.34 N/(214 kg) ≈ -6.12 m/s²

The net acceleration of the boat ≈ 6.12 m/s² downwards

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