Answer
The speed of the arrow as it leaves the bow is 43 m/s.
Work Step by Step
The work done by the string on the arrow will be equal to the kinetic energy of the arrow as it leaves the bow. Therefore,
$KE = Work$
$\frac{1}{2}mv^2 = Fd$
$v = \sqrt{\frac{2Fd}{m}}$
$v = \sqrt{\frac{(2)(105 ~N)(0.75 ~m)}{0.085 ~kg}}$
$v = 43 ~m/s$
The speed of the arrow as it leaves the bow is 43 m/s.