A Baseball Player

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?

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