Final answer:
Children can increase their maximum gravitational potential energy with each bounce by exerting a greater force during each jump.
Step-by-step explanation:
The child can increase his maximum gravitational potential energy with each bounce by exerting a greater force during each jump. When the child exerts a greater force, he gains more kinetic energy as he swings downward, which is then converted into greater potential energy as he swings upward. By pushing off the bed with more force, the child can reach a higher height and increase his maximum gravitational potential energy.