Question

A marathon runner completes a 42.188–km course in 2 h, 36 min, and 12 s. there is an uncertainty of 23 m in the distance traveled and an uncertainty of 3 s in the elapsed time. calculate the percent uncertainty in the distance.

Answer 1

The percentage uncertainty in the distance is 0.054%.

Uncertainty in a measurement measures the deviation of the measured values from the true value.

The distance d can be expressed in the form d+/-Δd, where Δd is the absolute uncertainty in the measurement of distance.

The percentage uncertainty  is given by,

$Percentage uncertainty=\frac{\Delta d}{d} *100$

The uncertainty in the measurement of distance is 23 m. Express the uncertainty in km.

$\Delta d =\frac{23 m}{1000 m/km} =0.023 km$

Calculate the percentage uncertainty in the distance.

$\frac{\Delta d}{d} *100 =\frac{0.023 km}{42.188 km} *100=0.054 %$

Thus, the percentage uncertainty in the measurement of distance is 0.054%