Answer
(a) F = 350 N
(b) $a = 1.3 ~m/s^2$
Work Step by Step
(a) If the speed is constant, then $a = 0 ~m/s^2$. Note that when the window washer pulls on the rope with a force $F$, there are two forces of $F$ pulling up on the system of the window washer plus the bucket.
$\sum F = ma$
$2F - mg = 0$
$2F = mg$
$F = \frac{mg}{2} = \frac{(72 ~kg)(9.80 ~m/s^2)}{2} = 350 ~N$
(b) If she increases the original force $F_0$ by 15%, the new force $F$ is (1.15)(350 N) which is 400 N.
$ma = \sum F$
$ma = 2F - mg$
$a = \frac{2F - mg}{m} = \frac{(2)(400 ~N) - (72 ~kg)(9.80 ~m/s^2)}{72 ~kg} = 1.3~m/s^2$
