In the American game of baseball, a pitcher throws a baseball, which is a round sphere of diameter b = 0.075 m, a distance of 18.4 m (60.5 feet), to a batter, who tries to hit the ball as far as he can. A baseball has a mass close to 0.15 kg. A radar gun measures the speed of a baseball at the time it reaches the batter at 44.7 m/s (100 mph). The drag coefficient c_d of a baseball is about 0.3. Give a semi-quantitative estimate of the speed of the ball when it left the pitcher’s hand by 

(a) Assuming that the ball’s speed is never too different from 100 mph to compute roughly how long it takes to go from the pitcher to the batter, 

(b) Using (a) to estimate the energy lost to air resistance, and (c) using 

(b) To estimate the original kinetic energy and velocity.