Bouncing to Balance: Unveiling Energy on the Trampoline - Exploring Kinetic Energy at Mid-Jump

To determine the kinetic energy of the kid when they come halfway down, we can use the principle of conservation of energy. At the top of the jump, all the energy is in the form of potential energy (1,000 J). When the kid is halfway down, some of this energy has been converted into kinetic energy, and the remaining energy is still potential energy. At the halfway point, the potential energy will be halved because potential energy is directly proportional to height. Therefore, the potential energy at this point is: \[ \frac{1000 \text{ J}}{2} = 500 \text{ J} \] Since the total mechanical energy is conserved, the sum of potential energy and kinetic energy remains constant at every point in the motion. Thus: \[ \text{Total Energy} = \text{Potential Energy} + \text{Kinetic Energy} \] \[ 1000 \text{ J} = 500 \text{ J} + \text{Kinetic Energy} \] Solving for kinetic energy: \[ \text{Kinetic Energy} = 1000 \text{ J} - 500 \text{ J} = 500 \text{ J} \] So, the kid will have 500 J of kinetic energy when they come halfway down: \[ \boxed{500 \text{ J}} \]