Question

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 seconds, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 seconds, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?

Answer 1

a) 2,650%

b) 27,400%

c) 164,900%

Explanation:

We want to measure the percentage we would have to increase the typical value to obtain the values given in a), b) and c).

But 0.2 increased in x% equals

0.2 + 0.2(x/100) =0.2(1+x/100)

So, if we want to increase 0.2 in x%, we must multiply it by (1+x/100)

a)

We need to find the value of x such that

0.2(1+x/100) = 5.5 ⇒ (1+x/100)=5.5/0.2 ⇒ 1+x/100=27.5

⇒ x/100=26.5 ⇒ x=2,650%

b)

0.2(1+x/100) = 55 ⇒ (1+x/100)=55/0.2 ⇒ 1+x/100=275

⇒ x/100=274 ⇒ x=27,400%

c)

5.5 min = 5.5*60 s = 330

0.2(1+x/100) = 330 ⇒ (1+x/100)=330/0.2 ⇒ 1+x/100=1,650

⇒ x/100=1,649 ⇒ x=164,900%