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?

Question

11.5 s +- 0.196 s
11.5 s +- 0.1955 s
11.5 s +- 0.2 s
11.5 s +- 0.19 s

Answer 1

To calculate the uncertainty in the time measurement, we need to apply the given percentage uncertainty to the measured time.

1. First, find the percentage uncertainty: \[ \text{Uncertainty} = \text{Measured Time} \times \left(\frac{\text{Uncertainty Percentage}}{100}\right) \]

2. Given:

   • Measured Time = 11.5 seconds
   • Uncertainty Percentage = 1.7%

3. Now, calculate the uncertainty: \[ \text{Uncertainty} = 11.5 , \text{s} \times \left(\frac{1.7}{100}\right) = 11.5 , \text{s} \times 0.017 = 0.1955 , \text{s} \]

4. We can round this result to an appropriate number of significant figures. Here, two decimal places give us: \[ 0.1955 , \text{s} \approx 0.2 , \text{s} \]

Thus, the total measurement with uncertainty is: \[ 11.5 , \text{s} \pm 0.196 , \text{s} \]

However, as we consider rounding to match the options provided in the question, we can express it as: \[ 11.5 , \text{s} \pm 0.2 , \text{s} \]

Thus, the answer is: 11.5 s ± 0.2 s