The racket applies an average acceleration of
[tex]a_{\rm ave} = \dfrac{\Delta v}{\Delta t} \\\\ a_{\rm ave} = \dfrac{40\frac{\rm m}{\rm s} - \left(-30\frac{\rm m}{\rm s}\right)}{5.2\,\rm ms} = \dfrac{40\frac{\rm m}{\rm s} - \left(-30\frac{\rm m}{\rm s}\right)}{0.0052\,\rm s} = 13,461.5\dfrac{\rm m}{\mathrm s^2}[/tex]
(Note that I'm taking the initial direction of the ball's motion to be negative.)
Then the average force exerted on the ball is
[tex]F_{\rm ave} = ma_{\rm ave} \\\\ F_{\rm ave} = (58.0\,\mathrm g)a_{\rm ave} = (0.058\,\mathrm{kg})a_{\rm ave} \approx \boxed{780\,\mathrm N}[/tex]
