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

Answer:

uncertainty in distance = 0.071 %

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

$percentage = \frac{25}{42188} \times 100$

$percentage = 0.06$%

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

$percentage = \frac{1}{9012} \times 100$

$percentage = 0.011$%

Since we know that

distance = (speed)(time)

so total percentage uncertainty is given as

$d = 0.06 + 0.011$

$d = 0.071$%