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 new stop watch will not be effective in timing the sprint team. The reason for the same is that the uncertainty in the stopwatch is too small to effectively differentiate between the sprint times.
If sprinters were timed with the new stopwatch, first sprinter's time would have been between = 12.04 - 0.05 and 12.04 + 0.05
= 11.99 and 12.09
or between the interval [11.99 , 12.09]
while the second sprinter's time would have been between
= 12.07 - 0.05 =and 12.07 + 0.05
= 12.02 and 12.12
or between the interval [12.0.2 , 12.12]
Hence, there is an overlap between the worst time of the first sprinter, that is, 11.99 and the best time of the second sprinter, that is, 12.02
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