Question

An 100 kg human decides to heat a 100,000 kg pool by jumping into it from a diving board. You may model the diving board as a vertical spring whose equilibrium position is level with the water’s surface. They compress this spring by d = 0.5 m prior to launch. The specific heat of liquid water is about 3187 J/kg K. Their landing heats up the water by 0.002° C. Throughout this problem, you may ignore air resistance. While the diving board is compressed, you may ignore gravitational potential energy. (But not after it’s decompressed to equilibrium!) You may take g ≈ 10 m/s2.

A) Assume that 90% of their kinetic energy just before landing goes into thermal energy of the pool water. What is the diving board’s spring constant?

B) What is their maximum height above the water’s surface?

C) Plot all changing mechanical energies from just after they’ve launched to when they reach their maximum height. Label all initial and final values.

Answer 1