Final answer:
The uncertainty of ±0.05 seconds in the new stopwatch is too great to accurately differentiate between the sprint times of high school athletes, where races can be won by margins smaller than the stopwatch's uncertainty.
Step-by-step explanation:
A high school track coach has just purchased a new stopwatch with an uncertainty of ±0.05 seconds. When considering the timing of sprints, this level of uncertainty can impact the accuracy of the measurements. During a track meet, where the difference between first and second place can be as little as a few hundredths of a second, an uncertainty of ±0.05 seconds is significant. For instance, when the first-place sprinter clocks in at 12.04 seconds and the second-place sprinter at 12.07 seconds, it is not possible to conclusively say who won if the timing was solely based on this particular stopwatch. The uncertainty of the stopwatch measurement is too great to effectively differentiate between such close sprint times. This is further complicated by human reaction time when starting and stopping the watch, which adds additional uncertainty beyond the inherent inaccuracy of the stopwatch itself.