- #1

lamerali

- 62

- 0

## Homework Statement

An Astronaut traveling at 0.90 c, with respect to Earth, measures his pulse adn finds it to be 70 beats per minute.

a) Calculate teh time required for one pulse to occur, as measured by the astronaut.

b) Calculate the time required for one pulse to occur, as measured by an Earth-based observer.

c) calaculare the astronaut's pulse, as measured by an Earth-based observer.

d) What effect, if any, would increasing the speed of the sapacecraft hav eon the astronaut's pulse as measured by teh astronaut and by the Earth observer? Why?

## Homework Equations

[tex]\Delta[/tex] t = [tex]\frac{\Delta t_o}{\sqrt{1 - \frac{ v^2 }{ c^2 }}}[/tex]

## The Attempt at a Solution

a)

(1 min / 70 pulses) x (60 sec) = 0.85 s

Therefore the astronaut feels a pulse every 0.85 s.

b)

[tex]\Delta[/tex] t = [tex]\frac{\Delta t_o}{\sqrt{1 - \frac{ v^2 }{ c^2 }}}[/tex]

[tex]\Delta[/tex] t_o = [tex]\Delta[/tex] t x [tex]\sqrt{1 - \frac{ v^2}{c^2}}[/tex]

[tex]\Delta[/tex] t_o = (0.85) x [tex]\sqrt{1 - \frac{ 0.90c^2}{c^2}}[/tex]

= 6 seconds

Therefore the time required for one pulse to occur as measured by an Earth-based observer is 6 seconds.

c) (60 seconds / 6 seconds) = 10 beats per second

Therefore the astronauts pulse as measured by an Earth-based observer is 10 beats per minute.

d) As the speed of the spacecraft increases the astronaut's pulse will increase from the frame reference of the astronaut. From the frame reference of the Earth observer the pulse of the astronaut will decrease.