The current theory of the structure of the
earth, called plate tectonics, tells us that the
continents are in constant motion. assume that the north american continent
can be represented by a slab of rock 5300 km on a side and 37 km deep and that the rock has an average mass density of 2720 kg/m^3.
the continent is moving at the rate of about 4.8 cm/year.
a) what is the mass of the continent? answer in units of kg
b) what is the kinetic energy of the continent? answer in units of j.
c) a jogger (of mass 77 kg) has the same kinetic energy as that of the continent. what would his speed be? answer in units of m/s.

Answers:

a)

b)

c)

Explanation:

Density  is defined as a relation between mass and volume :

(1)

Where:

is the average density of the continent

is the mass of the continent

is the volume of the continent, which can be estimated is we assume it as a a slab of rock 5300 km on a side and 37 km deep:

Finding the mass:

(2)

(3)

(4) This is the mass of the continent

Kinetic energy is given by the following equation:

(5)

Where:

is the mass of the continent

is the velocity of the continent

(6)

(7) This is the kinetic energy of the continent

If we have a jogger with mass and the same kinetic energy as that of the continent , we can find its velocity by isolating from (5):

(6)

Finally:

This is the speed of the jogger