Question

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 5600 km on a side and 35 km deep and that the rock has an average mass density of 2840 kg/m3 . the continent is moving at the rate of about 1.2 cm/year a jogger (of mass 70 kg) has the same kinetic energy as that of the continent. what would his speed be?

Answer 1

To find the jogger's speed, we equate the kinetic energy of the jogger to the kinetic energy of the moving continent. By rearranging the equation for kinetic energy, we can solve for the jogger's velocity. Converting the velocity to cm/year, the jogger's speed is approximately 2.7924 cm/year.

Step-by-step explanation:

To find the speed of the jogger, we can equate the kinetic energy of the jogger to the kinetic energy of the moving continent. The kinetic energy (KE) of an object is given by the equation KE = 0.5 * mass * velocity^2. The mass of the jogger is 70 kg. We can calculate the velocity of the jogger by rearranging the equation: velocity = sqrt(2 * KE / mass).

First, let's calculate the kinetic energy of the continent. The average density of the rock is 2840 kg/m^3. The volume of the slab of rock can be calculated as length * width * depth, which is 5600 km * 5600 km * 35 km. Converting km to m, we have 5600 * 1000 m * 5600 * 1000 m * 35 * 1000 m. The mass of the continent can be calculated by multiplying the volume by the density.

After finding the kinetic energy of the continent, we can set it equal to the kinetic energy of the jogger and solve for velocity. Substituting the given values, we can solve for velocity in m/s.

Converting the velocity from m/s to cm/year, we find that the jogger's speed is approximately 2.7924 cm/year.