The astronaut whose heart rate on Earth is 63 beats/min increases his velocity to v = 0.70c.Now what is his heart rate as measured by an Earth observer?
A)45 beats/min
B)88 beats/min
C)19 beats/min
D)90 beats/min
E)210 beats/min

Question

The astronaut whose heart rate on Earth is 63 beats/min increases his velocity to v = 0.70c.Now what is his heart rate as measured by an Earth observer?
A)45 beats/min
B)88 beats/min
C)19 beats/min
D)90 beats/min
E)​210 beats/min

Quizplus · Accepted Answer

The astronaut's heart rate will appear slower to an Earth observer due to time dilation, which is a consequence of special relativity. The formula for time dilation is $ t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} $, where $ t' $ is the dilated time, $ t $ is the proper time, $ v $ is the velocity of the moving object, and $ c $ is the speed of light. Since the astronaut's heart beats slower from the Earth observer's perspective, the observed heart rate decreases. Given the astronaut's velocity of $ 0.70c $, the calculation would show a decrease in the heart rate, making 45 beats/min the correct answer after applying the time dilation formula and adjusting for the context of the question.

The Astronaut Whose Heart Rate on Earth Is 63 Beats/min