From Potential to Kinetic: Calculating Energy Transfer on a Trampoline

Based on the principle of conservation of energy, the total mechanical energy of a system is constant if no external forces are acting on it. Therefore, the kid's potential energy at the top of the jump should be equal to their kinetic energy at the bottom. However, you are asking about halfway down the jump. Since energy is being conserved, if we let the trampoline surface to be the reference point (zero level of potential energy), we can say at the top (maximum height) the child has maximum potential energy and zero kinetic energy, since they are momentarily at rest. On their way down, potential energy is being converted into kinetic energy. At halfway down, not all potential energy is converted into kinetic energy, so the child will not have 1000J of kinetic energy yet. However, without knowing the total distance of the jump, it's impossible to determine the exact amounts of potential and kinetic energy the child will have halfway down. In reality, the potential to kinetic energy transfer isn't linear (it follows a parabolic curve). For a more precise calculation, further information like the specifics of the jump is required.