Answer
The increase in the gravitational potential energy of the ladder is 17.8 J.
Work Step by Step
We can find $h_1$, the height of the center of mass of the ladder when it is leaning at an angle of $53.0^{\circ}$. Let $L$ be the length of the ladder.
$h_1 = \frac{L}{2}~sin(53.0^{\circ})$
$h_1 = \frac{2.00~m}{2}~sin(53.0^{\circ})$
$h_1 = 0.7986~m$
We can find the increase in potential energy when the center of mass goes up to $h_2 = 1.00 ~m$.
$\Delta PE = PE_2-PE_1$
$\Delta PE = mg(h_2-h_1)$
$\Delta PE = (9.00~kg)(9.80~m/s^2)(1.00~m-0.7986~m)$
$\Delta PE = 17.8~J$
The increase in the gravitational potential energy of the ladder is 17.8 J.
