Eugenia wants to find out how fast she walked along the hiking trail that took h

Question

Eugenia wants to find out how fast she walked along the hiking trail that took her 1.5 h to complete (she didn’t have any way of measuring the time that passed during her walk any more precisely than that). 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 the measuring tape (the smallest division is 1 cm) and got 754cm, 748cm, 739cm. Find the length of her stride. What is the length of the hiking trail? What are absolute and relative uncertainties in that length?

Explanation / Answer

Average length she walked in 10 steps = (754 + 748 + 739)/3 = 747 cm.

Average length of her stride = 747/10 = 74.7 cm

Length of hiking trail = 10000*74.7 = 747000 cm = 7.47 km

Absolute uncertainity = {(75.4 - 74.7) + (74.8 - 74.7) + (74.7 - 73.9)}/3 = 0.533 cm which is less than least count so absolute uncertainity = 1 cm.

Relative uncertainity = 1/74.7 = 0.0134.

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