A marathon runner completes a 42.188-km course in 2 h, 40 min, and 13 s. There is an uncertainty of 29 m in the distance traveled and an uncertainty of 3 s in the elapsed time. (Express your answers to the correct number of significant figures and proper units.)

The missing part of the question is;

(a) Calculate the percent uncertainty in the distance.

(b) Calculate the percent uncertainty in the elapsed time.

(c) What is the average speed in meters per second?

(d) What is the uncertainty in the average speed?

Answer:

A) 0.0687%

B) 0.0312%

C) 4.389 m/s

D) 0.0044 m/s

Step-by-step explanation:

We are given;

Total Marathon distance = 42.188 km

Uncertain distance = 29m = 0.029 km

Time to complete marathon = 2 h, 40 min, and 13 s = 9613 seconds

Uncertain time = 3 seconds

A) % uncertainty in distance = (uncertain distance/total marathon distance) * 100% = (0.029/42.188) * 100% = 0.0687%

B) % uncertainty in the elapsed time = (elapsed time/total time) * 100% = (3/9613) * 100% = 0.0312%

C) average speed = total distance/total time

Total distance when converted to metres is 42188 m

Thus; average speed = 42188/9613 = 4.389 m/s

D) The percent uncertainty in the average speed is the combination of uncertainties of distance and time.

%uncertainty in speed = % uncertainty in distance + % uncertainty in the elapsed time

%uncertainty in speed = 0.0687% + 0.0312% = 0.0999%

Therefore, the uncertainty in the speed is;

δ_speed = 0.0999/100 * 4.389

δ_speed = 0.0044 m/s