Question

A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05s. 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?

Answer 1

the stopwatch has an uncertainty of ±0.05s.

Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s to 15.01 s

first-place sprinter came in at 12.04 s

with uncertainity now

T₁₊=12.04+0.05=12.09s

T_1-=12.04-0.05=11.99s

.range of first place sprinter is = (11.99s to 12.09s)

now for the second place sprinter

second-place sprinter came in at 12.07 s

with uncertainiy of stopwatch as

T₂₊=12.07+0.05s=12.12s

T_2-=12.07s-0.05s=12.02s

range of sceond place sprinter is =(12.02s to 12.12s)

thjere is a difference of 0.10 seconds between the best and worst performance of the sprinters so

No, coach’s new stopwatch not helpful in timing the sprint team , the uncertainty in the stopwatch is too great to effectively differentiate between the sprint times.

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