Question

An interstellar spacecraft is able to travel at a velocity of 0.600 c.

(a)An observer on the Earth reports an event on the spacecraft as tacking exactly 1.00 hr. How much time elapses on board the spacecraft according to the pilot of the spacecraft who promptly disagrees with the Earth observer?

(b)If your pulse rate on board the spacecraft is 72.0 beats a minute and this information is sent back to the Earth by radio, what does the Earth observer actually record as your pulse in beats a minute? Remember that pulse in beats/minute is frequency information which is the reciprocal of time information.

Answer 1

given

velocity of 0.600 C = v

a )

t = 1 hr

using equation t ' = t ( 1 - v²/C² )^1/2

= 1 x ( 1 - 0.6² C² /C² )^1/2   

= ( 1 - 0.6² C² /C² )^1/2   

= ( 1 - 0.6² )^1/2   

= 0.8 hr

or t ' = 0.8 x 60

t ' = 48 min

b )

no of beats = 72

spacecraft is 72.0 beats a minute

so t = 1 min

t ' = t ( 1 / ( 1 - v²/C² )^1/2 )

= 1 x ( 1 / ( 1 - 0.6² C² /C² )^1/2 )

= ( 1 / ( 1 - 0.6² C² /C² )^1/2)   

= ( 1 / ( 1 - 0.6² )^1/2 )

t ' = 1.25 min

the heart beat rate is = 72 / 1.25

= 57.6 meats/min