Final answer:
The accuracy of an umpire knowing the position of a baseball depends on the speed of the baseball and the percentage uncertainty in that speed. The formula Δx = v × Δt can be used to calculate the uncertainty in the position of the baseball. For example, if the umpire measures the position of the baseball over a time interval of 1 second, the uncertainty in the position would be 44.7 meters.
Step-by-step explanation:
The accuracy with which an umpire can know the position of a baseball depends on several factors, including the speed of the baseball and the percentage uncertainty in that speed.
Given that the baseball is moving at 100.0 mi/h ± 1.00% (44.7 m/s ± 1.00%), and assuming the umpire can accurately measure the speed, the uncertainty in the position of the baseball can be calculated using the formula:
Δx = v × Δt
where Δx is the uncertainty in the position, v is the velocity of the baseball, and Δt is the time interval over which the position is being measured.
For example, if the umpire measures the position of the baseball over a time interval of 1 second, the uncertainty in the position would be 44.7 m/s × 1 s = 44.7 meters.