Answer:
Heart rate=80 beats per minute
Uncertainty=3 beats per minute
Explanation:
We are given that a person measures heart beat by counting the number of beats in 30 s.
If number of beats=[tex]40\pm 1[/tex]
Time=[tex]30.0\pm 0.5[/tex]
We have to find the heart rate and its uncertainty in beats per minute
Maximum number of beats=40+1=41
Minimum time=30.0-0.5=29.5 s
Because when heart beat increases then time reduces.
We know that 1 minute =60 seconds
Therefore, time =[tex]\frac{29.5}{60}=0.492 minutes[/tex]
Average number of beats=40
Average time=30 seconds=[tex]\frac{30}{60}=0.5 minutes[/tex]
Heart rate =[tex]\frac{number\;of\;beats}{time}[/tex]
Heart rate =[tex]\frac{40}{0.5}=80 beats per minute[/tex]
Maximum heart rate=[tex]\frac{41}{0.492}=83.33 beats per minute[/tex]
When minimum number of beats=40-1=39
Maximum time=30.0+0.5=30.5 seconds
Because when heart beat slow then it takes more times
Time=[tex]\frac{30.5}{60}=0.508 minutes[/tex]
Minimum heart rate=[tex]\frac{39}{0.508}=76.77 beats per minute[/tex]
Uncertainty when heart rate is maximum
Uncertainty=83.33-80=3.33 beats per minute
Uncertainty when heart rate is minimum
Uncertainty=80-76.77=3.23 beats per minute
Average uncertainty=[tex]\frac{3.33+3.23}{2}[/tex]
Average uncertainty=3.28 [tex]\approx 3 [/tex]beats per minute
Hence, heart rate=80 beats per minute
Uncertainty=3 beats per minute
