After boarding the fisherman in a boat with vertical walls and a bottom area of 4 m2

After boarding the fisherman in a boat with vertical walls and a bottom area of 4 m2, the boat sank 20 cm into the water. Determine the fisherman’s weight.

S = 4 m2.

Δh = 20 cm = 0.2 m.

g = 10 m / s2.

ρ = 1000 kg / m3.

m -?

The force of gravity m * g of the fisherman who got into the boat is equal to the change in the buoyancy force of Archimedes ΔFarch: ΔFarch = m * g.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρ * g * V. Where ρ is the density of the liquid in which the body is immersed, g is the acceleration of gravity, V is the volume of the immersed part of the body in the liquid.

V = S * h, where S is the area of ​​the boat, h is the depth of immersion of the boat in the water.

ΔFarch = ρ * g * ΔV = ρ * g * S * Δh.

ρ * g * S * Δh = m * g.

The mass of the fisherman will be determined by the formula: m = ρ * S * Δh.

m = 1000 kg / m3 * 4 m2 * 0.2 m = 800 kg.

Since the mass of a fisherman cannot be so large, an error was made in the problem statement.

Answer: according to the condition of the problem, the mass of the fisherman is m = 800 kg.