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Problem 6 Medium Difficulty

An astronaut at rest on Earth has a heart rate of 70. beats/min. When the astronaut is traveling in a spaceship at 0.90$c,$ what will this rate be as measured by (a) an observer also in the ship and (b) an observer at rest on Earth?

Answer

a) 70 beats/min
b) 30 beats/min

Discussion

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AA

Alexis A.

March 10, 2021

Why is the proper time 60?

AA

Alexis A.

March 10, 2021

why is the proper time 60?

Video Transcript

heart rate of astronaut A crest on Earth is 70 beats, uh, per minute So heart rate of astronaut heart Uh, great oaf. Astronaut raped. Well, best remote astronaut it crest hit Risk. Uh, on Earth on hark is equal to 70 beats per minute. 70 beats per minute and speed of the astronaut. We is equal to zero point 90 times the speed off a light is the speed off astronaut. Let's sold park, eh? Well, heart rate measured by an observer in the spaceship. Um, we'll be the same. The heartbeat over the astronaut with the respect of other astronaut, Also in the ship will be 70 beats, uh, permanent. So, since both are in the same your efforts frame but therefore their relative relative, uh, speed is zero. Game four. The heart rate of astronaut ah will be 72 beats per minute. So hard trade Heart rate, uh, will be 70 beats per minute. 70 beats for a minute. Now, let's to part B mark B Well, heartbeat major by an observer. It dressed on earth. Uh, we know that Delta T It's equal to don't, uh, t proper. Divided by ah square Rudolph one minus. We squared, Divided by C square. Hear proper time is 60 seconds divided by square Rudo one minus ah, 0.9 Zito Times C square divided by cease were see school gets canceled, would see square and we have 60 seconds divided by, uh, squared Rudolph 0.19 And this gives us 1 37 1 37.61 point 61 seconds and in minutes, Delta T is equal to 2.29 minutes. And so heartbeat or rate off heart radio heartbeat So great. It's a cool too 70 divided by, uh, 2.29 And this gives us 30 bind 57 beats per minute for a minute.

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