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Answer :
Final answer:
The percent uncertainty in the distance is 0.0592%, the uncertainty in elapsed time is 1 s, the average speed is 4.68 m/s, and the uncertainty in average speed is 0.0031 m/s.
Explanation:
(a) To calculate the percent uncertainty in distance, we can use the formula: percent uncertainty = (uncertainty / measured value) * 100%. In this case, the uncertainty in distance is 25 m and the measured value is 42.188 km (which is equivalent to 42,188 m), so the percent uncertainty in distance is: (25 m / 42,188 m) * 100% = 0.0592%.
(b) To calculate the uncertainty in elapsed time, we simply need to use the given value of 1 s.
(c) Average speed is calculated by dividing distance by time. In this case, the distance is 42.188 km (or 42,188 m) and the time is 2 hours, 30 minutes, and 12 seconds (which is equivalent to 2*3600 + 30*60 + 12 = 9012 seconds). So the average speed is: 42188 m / 9012 s = 4.68 m/s.
(d) To calculate the uncertainty in average speed, we can use the formula: uncertainty in average speed = average speed * (percent uncertainty in distance + percent uncertainty in time). In this case, the average speed is 4.68 m/s, the percent uncertainty in distance is 0.0592%, and the percent uncertainty in time is (1 s / 9012 s) * 100% = 0.0111%. So the uncertainty in average speed is: 4.68 m/s * (0.0592% + 0.0111%) = 0.0031 m/s.
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Final answer:
- The percent uncertainty in the distance is 0.05922%
- The uncertainty in elapsed time is 1 s
- The average speed is 5.355 m/s
- The uncertainty in average speed is 0.0312 m/s.
Explanation:
(a) To calculate the percent uncertainty in the distance, we divide the uncertainty by the measured distance and multiply by 100.
Percent uncertainty in distance = (uncertainty in distance / distance) x 100
Percent uncertainty in distance = (25 m / 42188 m) x 100 = 0.05922%
(b) To calculate the uncertainty in the elapsed time, we simply take the given uncertainty.
Uncertainty in elapsed time = 1 s
(c) Average speed is calculated by dividing the distance traveled by the elapsed time. We convert the time to seconds and the distance to meters for consistency.
Average speed = distance / time
Average speed = 42188 m / 7872 s = 5.355 m/s
(d) To calculate the uncertainty in the average speed, we use the formula:
Uncertainty in average speed = (uncertainty in distance / distance) x average speed
Uncertainty in average speed = (25 m / 42188 m) x 5.355 m/s = 0.0312 m/s
Your question is incomplete, but most probably the full question was:
A marathon runner completes a 42.884 km course in 2 h, 11 min, and 52 s. What is the percent uncertainty in the distance, the uncertainty in elapsed time, the average speed, and the uncertainty in average speed?
