A marathon runner completes a 42.188 km course in 2 h, 29 min, and 21 s. There is an uncertainty of 23 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, 29 min, and 21 s. There is an uncertainty of 23 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?

(d) What is the uncertainty in the average speed? in m/s

Answer 1

Using definitions of percent uncertainties

a) (Δd/d)x100%=(23m/42188m)x100%=0.055% [2 sig.figs]

b) (Δt/t)x100%1s/(2x3600s+29x60s+21s)x100%=(1s/8961s)x100%=0.011% [2 sig.figs]

c) V_av=42188m/8961s=4.708m/s

d) Using the relative uncertainty of a ratio V_av=(d/t)

ΔV_av/V_av=(Δd/d)+(Δt/t)=0.055/100+0.011/100

=0.00066 ---> ΔV_av=V_av x (ΔV_av/V_av)=

=4.708m/s x0.00066=0.003m/s [1 sig.fig]