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A high school track coach has just purchased a new stopwatch that has an uncertainty of s. runners on the team regularly complete 100-m sprints in 12.49 s to 15.01 s. at the school’s last track meet, the first-place sprinter finished in 12.04 s and the second-place sprinter finished in 12.07 s. yes or no—will the coach’s new stopwatch be helpful in timing the sprint team? why or why not? no, the uncertainty in the stopwatch is too large to effectively differentiate between the sprint times. no, the uncertainty in the stopwatch is too small to effectively differentiate between the sprint times. yes, the uncertainty in the stopwatch is too large to effectively differentiate between the sprint times. yes, the uncertainty in the stopwatch is too small to effectively differentiate between the sprint times.

Answer :

A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05 s . Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s to 15.01 s . At the school’s last track meet, the first-place sprinter came in at 12.04 s and the second-place sprinter came in at 12.07 s .

No, the sprint team cannot be timed with the new stopwatch. The same is true; the stopwatch's margin of error is too small to distinguish between the sprint times accurately.

If sprinters were timed with the new stopwatch, the first sprinter's time would have been between [11.99, 12.00] or = 12.04 - 0.05 and 12.04 + 0.05 .09]

The time of the second sprinter would have ranged between [12.0.2, 12] and = 12.07 - 0.05, and 12.07 + 0.05, respectively.

As a result, there is overlap between the first sprinter's worst time of 11.99 and the second sprinter's best time of 12.02.

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