# 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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