A baseball bat strikes a ball when both are moving toward each other at $31\mathrm{.}3\frac{m}{s}.$ The bat and the ball are in contact for $1\mathrm{.}20$ ms $,$ after which the ball travels in the direction opposite to its initial direction at a speed of $42\mathrm{.}5\frac{m}{s}.$ The masses of the bat and ball are $850$ g and $145$ g $,$ respectively. What is the average force exerted by the bat on the ball?

A$.8920$ N

B$.3680$ N

C$.1350$ N

D$.4540$ N

E$.10700$ N