Question

A pitch may result in a strike if its height is between 2.5 and 5 feet when it crosses home plate. This range is called the batter's strike zone. The pitcher throws the ball from a height of 6 feet with an initial vertical velocity of 5 ft/s and a horizontal velocity of 116 ft/s. Can this pitch result in a strike?

Answer 1

Distance = the integral of velocity. The distance from the pitchers rubber to home plate is 60 feet and 6 inches, but, in reality, the ball is released about 59 feet from the plate.

Let h be the horizontal velocity and v the vertical velocity.

h(t) = 116t

∫ 116t dt = 58t^2 = 59

t is approximately 1 (second)

∫ 5 dt = 5t

So the ball started at 6 feet, reached the plate in 1 second still rising and thus was too high to be in the strike zone.

Answer 2

thanks cx

Answer 3

ur welcome :)