Afireman of 80 kg slides down a pole. when he reaches the bottom, 4.2 m below his starting point, his speed is 2.2 m/s . by how much has thermal energy increased during his slide?

3099 J

Explanation:

The increase in thermal energy corresponds to the mechanical energy lost in the process.

The mechanical energy is given by the sum of gravitational potential energy and kinetic energy of the fireman:

At the top of the pole, the fireman has no kinetic energy, so all his mechanical energy is just potential energy:

When the fireman reaches the bottom, he has no gravitational potential energy, so his mechanical energy is just given by his kinetic energy:

So, the loss in mechanical energy was

and this corresponds to the increase in thermal energy.

3. dark matter

empty space could also be a simple vacuum