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 . Will the coach’s new stopwatch be helpful in timing the sprint team? Why or why not?

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valetta valetta · Answer 1 · 2019-10-03T07:46:35+02:00

Answer:

The new stopwatch will not be that useful in timing the sprint team at the school's last track meet.

Step-by-step explanation:

Given:

Accuracy of the stopwatch = ± 0.05 s

The time of the first place sprinter = 12.04 s

The time of the second-place sprinter = 12.07 seconds

Now,

If sprinters were timed with the new stopwatch,

thus,

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

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 i.e 11.99 and the best time of the second sprinter i.e 12.02

Hence,

The new stopwatch will not be that useful in timing the sprint team at the school's last track meet.