A child€™s pogo stick (Fig P8.56) stores energy in a spring with a force constant of 2.50 0 104 N/m. At position A (xA = ─ 0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position B (xB = 0), the spring is relaxed and the child is moving upward. At position C, the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. (a) Calculate the total energy of the child€“stick€“Earth system if both gravitational and elastic potential energies are zero for x = 0. (b) Determine xC. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Calculate the child€™s maximum upward speed.

Figure P8.56