Question

Eugenia wants to find out how fast she walked along the hiking trail that took her 1.5 h to complete. She counted the number of steps with a pedometer and got 10000 steps. in order to calculate the distance she walked she estimated the length of her stride. she walked 10 steps three times at her usual rate and measured the distance with a measuring tape (the smallest division is 1cm) and got 745cm, 748 cm, 739 cm. Find the length of her stride. What is the length of the hiking trail? What are absolute and relative uncertainties in that length?

Answer 1

1) length of her stride

- 745/10 = 74.5

- 748/10 = 74.8

-739/10 = 73.9

Average: 74.5 + 74.8 + 73.9]/3 = 74.4 cm

2) length of the hiking trial

74.4 cm/step * 10,000steps = 744,000 cm = 7,440 m = 7.4 km

3) Absolute error

legnth with the smallest step measure: 73.9 * 10,000 = 739,000 cm

length with the largest step measure: 74.8 * 10,000 = 748,000 cm

maximum error 744,000cm - 739,000cm = 5,000 cm

4)  relative error

[absolute error / measure] * 100

[5,000 cm / 744,000 cm] * 100 = 0.67%