Aswimmer finds that she just floats in water. if she weighs 70
kg what is her volume (ρwater = 1×103 kg m−3)?

Explanation:

Density is a physical characteristic property of matter that establishes a relationship between the mass  of a body or substance and the volume  it occupies. Mathematically is expressed as:

(1)

We already know the mass of the swimmer, which is and the density of water .

The volume can be found t by the Archimedes' Principle, which states the following:  

A body totally or partially immersed in a fluid at rest (water in this case), experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

Hence, the volume of the swimmer is equal to the volume her body displaces. This means we only a have to isolate from (1):

(2)

(3)

Finally:

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day