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**exam help!!**

Hydrostatics

1. Homework Statement

A girl of mass 40 kg and volume of 40 liter wants to keep her head of volume 3 liter above water surface as she can't swim . how much air in Kg should she fill in her jacket??

2. Homework Equations

3. The Attempt at a Solution

mass of girl (m) = 40 kg

volume of girl (V) = 0.04 m^3(meter cube)

density of girl (D) = m / V = 1000 kg/m^3

volume of head (v') =0.003 m^3

let the mass of air in kg be x then

total mass of body = 40 + x

mass of water displaced = 40 + x

volume of water displaced = 1000(40 + x)

then

volume of immersion = V - v' = .04- .003 = .397

therefore from principle of flotation

volume of water displaced = volume of immersion of floating body

40000 + 1000x = .397

x=.397-40000 = -ve value

is my method correct??? and as " density of body = density of water " will require extra air to float.