Final answer:
A coach's new stopwatch with an uncertainty of ±0.05 seconds may not effectively differentiate between highly competitive sprint times, such as those within 0.03 seconds of each other, due to the margin of uncertainty being close to or exceeding the time difference between sprinters.
Step-by-step explanation:
The typical duration of a sprint in the inception phase is not precisely mentioned in the provided excerpts, but we can discuss the relevance and utility of a coach's new stopwatch for timing sprinters. A high school track coach's new stopwatch has an uncertainty of ±0.05 seconds. This means that when timing runners who perform 100-meter sprints ranging from 11.49 seconds to 15.01 seconds, the uncertainty margin could potentially affect the ability to distinguish between runners' times, particularly in close races like the one where the first-place finisher had a time of 12.04 seconds and the second-place sprinter had a time of 12.07 seconds. With a margin of uncertainty that slightly exceeds the difference between these two sprinters, the stopwatch's precision could be called into question.In conclusion, while the new stopwatch may provide a general timing for the sprinters, its ±0.05 seconds uncertainty might be too great to effectively differentiate between sprint times that are very close to one another. Therefore, the coach should consider the uncertainty of the stopwatch when evaluating performance during training or competitions.