In a hard pool shot, the cue ball may hit a numbered ball at $14\mathrm{.}5$ mph head$-$on$,$ coming to a dead stop. The time of impact is $0\mathrm{.}3$ ms and the mass of the ball is $0\mathrm{.}0117$ slug. Calculate the peak force between the balls during the collision. Round the final answer to the nearest whole number.