Question

A woman floats in a region of the Great Salt Lake where the water is about four times saltier than the ocean and has a density of about 1130 kg/m3. The woman has a mass of 52 kg, and her density is 943 kg/m3 after exhaling as much air as possible from her lungs.

1) Determine the percentage of her volume that will be above the waterline of the Great Salt Lake.

Answer 1

To develop the problem it is necessary to use the concepts related to density and its definition with respect to mass and volume, as well

`\rho= (m)/(V)`

Therefore to calculate the volume of woman:

`V = (m)/(\rho)\\V = (52)/(943)\\V = 0.0551 m^3`

Now, volume of water of Great Salt Lake with the mass of 52 kg,

`V_i = (52)/(1130) \\V_i = 0.0460 m^3`

So, percentage of her volume changed will be,

`\%=((V - Vi))/(V)*100\\\% = ((0.0551 - 0.0460))/(0.0551)*100 \\\% == 16.51 \%\\`

Therefore the percentage of her volume that will be above the waterline of the Great Salt Lake is 16.51%