Question

You are trying to measure the width of a sidewalk, but you measure the distances from the street to each side of the sidewalk. If you measure the far side of the sidewalk to be 49.8±0.13 m from the street and you measure the near side of the sidewalk to be 48.9±0.44 m from the street, what is the width and uncertainty of the width of the sidewalk?

Answer 1

The width of the sidewalk is 0.9 meters with an uncertainty of 0.57 meters, calculated by subtracting the near side measurement from the far side and then adding their uncertainties.

Step-by-step explanation:

To calculate the width and uncertainty of the width of a sidewalk based on measurements taken from the street to each side of the sidewalk, you need to subtract the near side measurement from the far side measurement. The measured distance to the far side of the sidewalk is 49.8 m with an uncertainty of 0.13 m, and the distance to the near side is 48.9 m with an uncertainty of 0.44 m.

Width of sidewalk = Far side measurement - Near side measurement = 49.8 m - 48.9 m = 0.9 m.

To find the combined uncertainty, you add the absolute uncertainties of the two measurements (since when you subtract quantities, the uncertainties add up). The total uncertainty is thus 0.13 m + 0.44 m = 0.57 m.

Therefore, the width of the sidewalk and its uncertainty is given by 0.9 ± 0.57 meters.