Question

(a) What is the density (in 0 decimal place) of a woman who floats in freshwater with 4.00% of her volume above the surface?

(b) What percent (in 2 decimal places) of her volume is above the surface when she floats in seawater?

Answer 1

(a) From the equilibrium of the force of gravity and the buoyancy force:

$$\rho_\text{liquid} gV(1-\kappa)=\rho_\text{body}gV,\\ \rho_\text{body}=\rho_\text{liquid} (1-\kappa)=690\text{ kg/m}^3.$$

(b) Reasoning the same way:

$$\rho_\text{seawater} (1-\kappa)=\rho_\text{body},\\ \kappa=1-\frac{\rho_\text{body}}{\rho_\text{seawater}}=0.0625,$$

or 6.25%.