Question

A person measures her heart rate by counting the number of beats in 30 s. If 36 ± 2 beats are counted in 30.0 ± 0.4 s, what is the heart rate and its uncertainty in beats per minute?

Answer 1

For the heart rate :

n = number of heat beats = 36

t = time taken to measure = 30 s = 30/60 min = 0.5 min (since 1 min = 60 sec)

R = heart rate

Heart rate is given as

`R = (n )/(t)`

inserting the values

`R = (36 )/(0.5)`

R = 72 min⁻¹

For uncertainty :

Δn = uncertainty in number of heat beats = ± 2

Δt = uncertainty in time taken = ± 0.4 s = ± 0.4/60 min = ± 0.0067 min (since 1 min = 60 sec)

ΔR = uncertainty in heart rate

uncertainty in Heart rate is given as

`(\Delta R)/(R)=\pm \left ( (\Delta n)/(n) + (\Delta t)/(t)\right )`

inserting the values

`(\Delta R)/(72)=\pm \left ( (2)/(36) + (0.0067)/(0.5)\right )`

ΔR = ± 4.96 min⁻¹