A track coach measures the 100 meter time of a track athlete. The runner completes the distance in 11.5 seconds. If the stopwatch has an uncertainty of 1.7%, what is the amount of uncertainty in the time? (1 point)

Question

A 11.5 +/- 0.003 s
B 11.5 +/- 0.34 s
C 11.5 +/- 0.2 s
D 11.5 +/- .17 s

Answer 1

To calculate the amount of uncertainty in the time based on the given percentage uncertainty, we can use the formula:

\[ \text{Uncertainty} = \text{Measured Value} \times \left(\frac{\text{Percentage Uncertainty}}{100}\right) \]

Here, the measured value is 11.5 seconds and the percentage uncertainty is 1.7%.

Calculating the uncertainty:

\[ \text{Uncertainty} = 11.5 , \text{s} \times \left(\frac{1.7}{100}\right) = 11.5 , \text{s} \times 0.017 = 0.1955 , \text{s} \]

Rounding this to two decimal places, we get approximately:

\[ \text{Uncertainty} \approx 0.20 , \text{s} \]

Thus, the amount of uncertainty can be expressed as:

\[ 11.5 \pm 0.2 , \text{s} \]

So the correct answer is:

C 11.5 +/- 0.2 s.