A Baseball Player

Classical Mechanics Level 3

A pitcher throws a baseball towards home plate, a distance of $18 \text{ m}$ away, at $v = 40 \text{ m}/\text{s}$ . Suppose the batter takes $.2 \text {s}$ to react before swinging. In swinging, the batter accelerates the end of the bat from rest through $2 \text{ m}$ at some constant acceleration $a$ . Assuming that the end of the bat hits the ball if it crosses the plate within $. 05 \text{ s}$ of the ball crossing the plate, what is the minimum required $a$ in $\text{m}/\text{s}^2$ to the nearest tenth for the batter to hit the ball?