Question

(a) A person's "resting" heart rate is his or her normal heart rate measured while sitting still (and long after doing anything physically exerting). A nurse on Earth measures the resting heart rate of a patient as 66.0 beats/min. Imagine the patient travels aboard a spaceship moving with a constant speed of 0.89c with respect to the Earth. What would be the patient's resting heart rate (in beats/min) as measured by someone else aboard the ship? beats/min

(b) Imagine an observer on Earth could measure the resting heart rate of the patient traveling aboard the spaceship. What rate (in beats/min) would the observer on Earth measure? beats/min

Answer 1

(a) As the observer on the ship is in the same reference frame as the patient, the heart rate will be the same.

66 beats / min

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(b) The time dilation equation is given as

t = t_p / sqrt ( 1 - v² / c²)

where t_p is the proper time

proper time is the time which is measured by an observer who is present at the start and end of event means the patient aboard the ship measures proper time as he is present on the ship at all times.

so,

t = 1/66 / sqrt (1 - 0.89² c² / c²)

c² will get cancel, we get

t = 1/66 / sqrt (1 - 0.89²)

t = 0.0151515 / 0.45596

t = 0.03322

so,

rate = 1/0.03322

rate = 30.1 beats / min

you can round it off to 30 beats / min ( as it should be an integer)