Throwing heat. In professional baseball, most pitchers can throw a fastball at a speed of 90 mi/h. For simplicity, assume the pitcher releases the ball just above the center of the pitcher’s mound. 

(a) Given that the regulation distance from the pitcher’s mound to home plate is 60.5 ft, how long does it take the ball to reach home plate after the ball leaves the pitcher’s hand? 

(b) It takes (on average) 0.20 s for the batter to get the tip of his bat over home plate. How much time does that give him to react? 

(c) The average fast pitch in professional women’s softball is about 60 mi/h, where the regulation distance from the pitcher’s mound to home plate is 40.0 ft. How do the travel time of a pitched ball and reaction time of a batter in softball compare with those in baseball? Keep three significant figures in your calculation.