Answer
$16, 245 ft-lbs $
Work Step by Step
The magnitude of the gravitational force acting on the man plus the can of paint is equal to $=(160+m)lbs$
Since, we are moving in the upward direction
$F \cdot dr=(185-\dfrac{9r}{s}) dr$
Work done, $W=\int_C F\cdot dr= \int_0^s (185-\dfrac{9r}{s}) dr$
Since $C$ shows a vertical line segment connecting the bottom and top of the silo, thus we have
Work done, $W=\int_C F\cdot dr=[185r-\dfrac{9r^2}{2s}]_0^s=185 s-4.5 s =16, 245 ft-lbs $
