A baseball $($m $=153$ g$)$ approaches a bat horizontally at a speed of $40\mathrm{.}2$ m$/$s $(89\mathrm{.}9$ mi$/$h$)$ and is hit straight back at a speed of $52\mathrm{.}1$ m$/$s $(117$ mi$/$h$).$ If the ball is in contact with the bat for a time of $1\mathrm{.}83$ ms$,$ what is the average force exerted on the ball by the bat? Neglect the weight of the ball, since it is so much less than the force of the bat. Choose the direction of the incoming ball as the positive direction.