Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 127

Rising fast ball. A batter in a baseball game will sometimes describe a pitch as being a rising ball, termed a hop. Although technically possible, such upward motion would require a large backspin on the ball so that an aerodynamic force would lift the ball. More likely, a rising ball is an illusion stemming from the batter’s misjudgment of the ball’s initial speed. The distance between the pitching rubber and home plate is \(60.5\text{ ft}\). If a ball is thrown horizontally with no spin, how far does it drop during its flight if the initial speed \(v_0\) is (a) \(36\text{ m/s}\) (slow, about \(80\text{ mi/h}\)) and (b) \(43\text{ m/s}\) (fast, about \(95\text{ mi/h}\))? (c) What is the difference in the two displacements? (d) If the batter anticipates the slow ball, will the swing be below the ball or above it?