A marathon runner completes a 42.188 km course in 2 h, 27 min, and 11 s. There is an uncertainty of 27 m in the distance traveled and an uncertainty of 1 s in the elapsed time.

Question

A marathon runner completes a 42.188 km course in 2 h, 27 min, and 11 s. There is an uncertainty of 27 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (Give all answers to the appropriate number of significant figures. Note that uncertainties should be reported to one significant figure and percent uncertainties should be reported to two significant figures.)

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? 

= ?m/s

d) What is the uncertainty in the average speed? 

= ?m/s

Answer 1

To calculate the uncertainty of your measurements, you'll need to find the best estimate of your measurement and consider the results when you add or subtract the measurement of uncertainty.

https://www.wikihow.com/Calculate-Uncertainty

a) Calculate the percent uncertainty in the distance.

(27 m/ 42,188 m)*100%=0.00064*100%=0.064%

b) Calculate the percent uncertainty in the elapsed time. 

[11 s/(2*3600+27*60+11 s)]*100%= 0.00124*100=0.124 %≈0.12%

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

42,188 m/ 8,831 =4.77 m/s

d) What is the uncertainty in the average speed?  = ?m/s To divide uncertain measurements, simply divide the measurements while adding their RELATIVE uncertainties.

Then V_av=4.77 m/s ± (0.00064+0.00124)=4.77±0.00188 m/s≈4.8±0.0019