In professional baseball, pitchers can throw a fastball at a speed of 90 mi/h. (
ID: 1652825 • Letter: I
Question
In professional baseball, pitchers can throw a fastball at a speed of 90 mi/h.
(a) Given that the regulation distance from the pitcher’s mound to home plate is 51 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) 0.27 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 33.5 ft. How long does it take the softball to reach home plate? For simplicity, assume the pitcher releases the ball just above the center of the pitcher’s mound
Explanation / Answer
a] Speed of the ball = 90mi/h = 40.2336 m/s
distance covered by the ball = 51 ft = 15.5448 m
therefore, the time it takes for the ball to reach the home plate = t = D/v = 15.5448/40.2336 = 0.3864 s.
b] Time for reaction will be: 0.3864 - 0.27 = 0.1164s.
c] speed of the ball = v = 60 mi/h = 26.8224 m/s
distance = 33.5 ft = 10.2108 m
therefore, time it takes for the ball to reach home plate will be: t = 10.2108/26.8224 = 0.3807s.