Final answer:
The work done by the gymnast while jumping on a trampoline is obtained by calculating the elastic potential energy stored in the trampoline's spring during compression; this is 234 Joules, indicating the energy used to lift the gymnast to the jump height.
Step-by-step explanation:
The question involves determining the work done by a gymnast during a jump on a trampoline, given the mass of the gymnast, the spring constant of the trampoline, the distance the trampoline is compressed, and the jump height achieved. The work done by the gymnast is the energy transferred to compress the spring of the trampoline, which can be calculated using the formula for the elastic potential energy stored in a compressed spring: ½kx², where k is the spring constant and x is the compression distance. In this case, the work done is ½(1300 N/m)(0.6 m)² = 234 J. Since work is energy transferred over time, we can conclude that all this energy is used to lift the gymnast to a height of 2.3m, against Earth's gravity, ultimately related to the gymnast's gravitational potential energy.