Answer:
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
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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