An astronaut at rest has a heart rate of 65 beats/min.What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.80c?
A) 108 beats/min
B) 39 beats/min
C) 81 beats/min
D) 52 beats/min

Question

Quizplus · Accepted Answer

We can use the time dilation formula, which states that the observed time interval is equal to the proper time divided by the Lorentz factor, to find the heart rate as measured by an earth observer. The Lorentz factor can be calculated as gamma = 1 / sqrt(1 - v^2/c^2), where v is the speed of the spaceship as a fraction of the speed of light (0.80c in this case) and c is the speed of light.

gamma = 1 / sqrt(1 - (0.80c)^2/c^2) 
gamma = 1.67

The observed heart rate can be found by dividing the proper heart rate (65 beats/min) by gamma:

observed heart rate = proper heart rate / gamma 
observed heart rate = 65 beats/min / 1.67 
observed heart rate ≈ 39 beats/min

Therefore, the astronaut's heart rate as measured by an earth observer will be 39 beats/min, which is closest to choice B.

An Astronaut at Rest Has a Heart Rate of 65