College Physics Problem 1.21

A person measures his or her heart rate by counting the number of beats in 30 s. If 40±1  beats are counted in 30±0.5 s, what is the heart rate and its uncertainty in beats per minute?

SOLUTION:

In order to compute for the heart rate in beats per minute, we need to solve for the base. The base is

frac{40  beats}{30.0  seconds}=frac{60.0  seconds}{1.00  min}=80  beats/minute

Then we compute for the percent uncertainty by combining the uncertainties of the number of beats and time. That is

%uncertainty=frac{1  beat}{40  beats}times100%  +frac{0.5  s}{30.0  s}times100%

%uncertainty=2.5%+1.7%

%uncertainty=4.2%

Based on this percent uncertainty, we compute for the tolerance

delta_{A}=frac{%uncertainty}{100  %}times A

delta_{A}=3.3  beats/min

Therefore, the heart rate is

80 pm 3  beats/min

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