The current theory of the structure of the

Question

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 4400 km
on a side and 33 km deep and that the rock
has an average mass density of 2870 kg/m3
.
The continent is moving at the rate of about
4.2 cm/year.
A jogger (of mass 76 kg) has the same kinetic
energy as that of the continent.
What would his speed be?
Answer in units of m/s.

Answer 1

First, we need to calculate the kinetic energy of the continent.

The mass (m) of the continent can be calculated by multiplying the density (ρ) with the volume (V):

m = ρ * V

The volume (V) of the continent can be calculated by multiplying the length (l), width (w), and depth (d):

V = l * w * d

Using the given values, we can calculate the volume:

V = 4400 km * 4400 km * 33 km
V = 6525600000000 m^3

Now, we can calculate the mass of the continent:

m = 2870 kg/m^3 * 6525600000000 m^3
m = 1.8727272 * 10^16 kg

The kinetic energy (KE) of an object can be calculated using the formula:

KE = (1/2) * m * v^2

We are given that the jogger has the same kinetic energy as the continent, so we can equate the two equations:

(1/2) * m * v_jogger^2 = (1/2) * m * v_continent^2

Simplifying the equation:

v_jogger^2 = v_continent^2

Taking the square root of both sides to solve for v_jogger:

v_jogger = v_continent

The given rate of movement of the continent is 4.2 cm/year. We need to convert this to m/s:

v_continent = 4.2 cm/year * (1 m/100 cm) * (1 year/365 days) * (1 day/24 hours) * (1 hour/3600 seconds)
v_continent = 1.33 * 10^-10 m/s

Now, we can calculate the speed of the jogger:

v_jogger = 1.33 * 10^-10 m/s

Therefore, the speed of the jogger would be approximately 1.33 * 10^-10 m/s.