I think the answer is Geothermal energy.
Mechanical energy E = mgh + 1/2mv²
When he starts, let h = 0 ⇒ E₁ = 1/2mv₁²
When he reaches height h ⇒ E₂ = mgh + 1/2mv₂²
Without friction, energy is conserved at all times.
E₁ = E₂
↓
1/2mv₁² = mgh + 1/2mv₂²
↓
1/2v₁² = gh + 1/2v₂²
↓
gh = 1/2(v₁² - v₂²)
↓
h = (v₁² - v₂²) / (2g)
The boundary between the crust and mantle is marked by a seismic-velocity discontinuity is called Mohorovicic discontinuity.
Mohorovicic discontinuity was discovered by Andrija Mohorovicic in 1909 who was a Croatian seismologist. He realized that the velocity of a seismic wave is related to the material's density where it is moving through. He decoded that the acceleration of the seismic waves that are observed within outer shell of the earth is a compositional change. Thus, the acceleration should be caused by a material of higher density.
