#### Answer

(a) As the child slides down to a lower height, the potential energy decreases as the potential energy is transformed into kinetic energy of the child's motion and thermal energy on the slide and the child's pants. Note that the amount of thermal energy produced is equal to the magnitude of the work done by friction.
(b) The thermal energy of the slide and the child's pants increases by 548 J.

#### Work Step by Step

(a) As the child slides down to a lower height, the potential energy decreases as the potential energy is transformed into kinetic energy of the child's motion and thermal energy on the slide and the child's pants. Note that the amount of thermal energy produced is equal to the magnitude of the work done by friction.
(b) The amount of thermal energy produced is equal to the magnitude of the work done by friction. We can use the work-energy theorem to find the work done by friction.
$PE + W_f = KE$
$W_f = KE - PE$
$W_f = \frac{1}{2}mv^2-mgh$
$W_f = \frac{1}{2}(20~kg)(2.0~m/s)^2-(20~kg)(9.80~m/s^2)(3.0~m)$
$W_f = -548~J$
The thermal energy of the slide and the child's pants increases by 548 J.