91影视

• The density of the body $\left({蚁}_b\right)=0.95$times the density of the water $\left({蚁}_w\right)$.
• The density of the quicksand $\left({蚁}_q\right)=6$times the density of the water $\left({蚁}_w\right)$.

By equating the buoyant force and weight of the fluid displaced by the body, we can find the relation ${\mathit{V}}_{\mathbf{f}}{\mathit{蚁}}_{\mathbf{f}}\mathbf{=}{\mathit{V}}_{\mathbf{b}}{\mathit{蚁}}_{\mathbf{b}}$. Using this, we can find the fraction of the body's volume above the fluid surface.

Formula:

Fraction $=\frac{Vb-Vf}{Vb}$

$=1-\frac{Vt}{Vb}$

$V_f{蚁}_f=V_b{蚁}_b$

Fraction $=1-\frac{V_f}{V_b}$ (1)

Buoyant force $\left(F_b\right)=$weight of the fluid displaced by the body $\left(F_w\right)$

$V_f{蚁}_{f}g=V_b{蚁}_{b}g$

Rearranging the equation,

$\frac{Vf}{Vb}=\frac{蚁b}{蚁f}$

Using in above equation (1),

Fraction $=1-\frac{蚁b}{蚁f}$

$=1-\frac{0.95蚁W}{蚁w}$

$=1-0.05$

$=0.05$

Fraction of the body's volume above the water surface is$0.05$

Fraction $=1-\frac{蚁b}{蚁q}$

Using given values,

Fraction $=1-\frac{0.95蚁\mathrm{w}}{1.6蚁\mathrm{w}}$

$=1-0.593375$

$=0.4062$

$鈮�0.41$

Fraction of the body's volume above the quicksand surface is$0.41$

From part $b,0.41$of the total human body will be above the quicksand. As the human body is less dense than quicksand, a person would sink to their chest and then float. Hence a person can breathe.