Question

Q3. 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?
A. 11.5 s ± 0.19 s
B. 11.5 s plus or minus 0.19 s
C. 11.5 s ± 0.20 s
D. 11.5 s plus or minus 0.20 s
E. 11.5 s ± 0.1955 s
F. 11.5 s plus or minus 0.1955 s
G. 11.5 s ± 0.196 s

Answer 1

To calculate the uncertainty in the time measured by the stopwatch, you can follow these steps:

1. Calculate the uncertainty based on the percentage uncertainty given:

\[
\text{Uncertainty} = \text{Percentage Uncertainty} \times \text{Measured Value}
\]

In this case:
- Percentage Uncertainty = 1.7% = 0.017 (as a decimal)
- Measured Value = 11.5 seconds

2. Now, calculate the uncertainty:

\[
\text{Uncertainty} = 0.017 \times 11.5 \, \text{s} = 0.1955 \, \text{s}
\]

3. Round the uncertainty to an appropriate number of significant figures. Since the measured time (11.5 seconds) has three significant figures, we would typically round the uncertainty to two or three significant figures. Here, we can express it as:

\[
11.5 \, \text{s} \pm 0.196 \, \text{s}
\]

Thus, the correct option is:

**G. 11.5 s ± 0.196 s**