Question

collegephysicsanswers A marathon runner completes a 42.188km course in 2h, 30 min, and 12s. There is an uncertainty of 25m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance.

Answer 1

uncertainty in distance = 0.071 %

Step-by-step explanation:

Distance covered by the marathon runner is given as

`d = 42.188 km`

uncertainty in the distance moved by runner is given as

`\Delta x = 25 m`

now we have

`d = (42188 \pm 25) m`

now percentage uncertainty in the distance is given as

`percentage = (25)/(42188) * 100`

`percentage = 0.06`%

now we have total time taken by him

`t = 2 h 30 min 12 s`

`t = 2(3600) + 30(60) + 12 = 9012 s`

now percentage uncertainty in time is given as

`percentage = (1)/(9012) * 100`

`percentage = 0.011`%

Since we know that

distance = (speed)(time)

so total percentage uncertainty is given as

`d = 0.06 + 0.011`

`d = 0.071`%