A slide in a park possesses a total length of 10 ext m and a height...

Let the boy be considered as a point mass since the work done by internal forces is neglected.

The boy starts from rest at the bottom and comes to rest at the top, so the change in his kinetic energy is zero, $\Delta K = 0$.

The external forces acting on the boy are the downward force of gravity and the upward force exerted by the ladder.

The work done by gravity as the boy ascends a height $h = 8.0 \text{ m}$ is given by:

$W_{g} = -mgh$

Since the boy's weight is $mg = 200 \text{ N}$, the work done by gravity is:

$W_{g} = -200 \times 8.0 = -1600 \text{ J}$

Applying the work-energy theorem:

$W_{\text{net}} = \Delta K$

$W_{\text{ladder}} + W_{g} = 0$

$W_{\text{ladder}} - 1600 = 0$

$W_{\text{ladder}} = 1600 \text{ J}$