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Physics

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A shipwrecked mariner is stranded on a desert island. He seals a plea for rescue in a 1.00 liter bottle, corks it up, and throws it into the sea. If the mass of the bottle, plus the message and the air inside, is 0.454 kg, what percentage of the volume of the bottle is submerged as it bobs away? Take the density of seawater to be 1030 kg/m3. For simplicity, assume the bottle and its contents have a uniform density.

  • Physics -

    Convert density of bottle and water to
    the same units.

    Db = 0.454kg/Liter
    Db = 0.454kg/1000cm^3
    Db = 454.*10^-6kg / cm^3. = Density of bottle.
    Vb = 1 Liter = 1000 cm^3. = Vol. of bottle.

    Dw = 1030kg/m^3
    Dw = 1030kg/10^6cm^3
    Dw = 1030*10^-6kg/cm^3. = Density of the water.

    Vs = (Db/Dw)* Vb
    Vs=(454*10^-6/1030*10^*1000cm^3=441cm^3
    Vol. submerged.

    %Vs=(Vs/Vb)*100%=(441/1000)*100%=44.1%.

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