Question

A healthy astronaut's heart rate is 60 beats/min. Flight doctors on Earth can monitor an astronaut's vital signs remotely while in flight.How fast would an astronaut be flying away from Earth if the doctor measured her having a heart rate of 21 beats / min

?

Answer 1

2.81 x 10⁸ m/s

Step-by-step explanation:

R₁ = rate of heartbeat on earth = 60 beats/min

T₁ = Time period for 1 beat on earth = 1/R₁ = 1/60 min = 60/60 sec = 1 sec

R₂ = rate of heartbeat on location of astronaut = 21 beats/min

T₂ = Time period for 1 beat at the location of astronaut = 1/R₂ = 1/21 min = 60/21 sec

v = speed of astronaut

c = speed of light = 3 x 10⁸ m/s

Using the equation

T₁ = T₂ sqrt(1 - (v/c)²)

1 = (60/21) sqrt(1 - (v/(3 x 10⁸))²)

v = 2.81 x 10⁸ m/s

Answer 2

GIVEN:
60 beats per minute
21 beats per minute
find x= how fast would an astronaut be flying away
1 x
----- * ------ = (60x = 21) -------> 60x = 21 ------------> x= 0.35
60 21 ------- -----
60 60

The answer is 0.35 seconds which refers to how fast would an astronaut be flying away from the earth if he has a heart rate of 21 beats/min.