Final answer:
The change in gravitational potential energy as the child descends the slide is 1750 J, and after accounting for the work done against friction, the child's final kinetic energy at the bottom of the slide is 450 J.
Step-by-step explanation:
The weight of a child is 250 N on a slide that is 7.0 m high. The work done against friction is 1300 J. To find the change in gravitational potential energy (GPE), the formula GPE = m*g*h is used, where m is the mass of the child, g is the acceleration due to gravity (9.8 m/s2), and h is the height. Here, GPE = weight * height because weight is the force of gravity on the child. Therefore, the initial GPE at the top of the slide is 250 N * 7.0 m = 1750 J.
As the child slides down, this potential energy is converted into kinetic energy (KE) and work done against friction. The final kinetic energy is the remaining energy after subtracting the work done against friction from the initial gravitational potential energy. So, the final kinetic energy KE = GPE - work done against friction = 1750 J - 1300 J = 450 J.