How Does Time Dilation Affect Dinner Time on a Starship Traveling at 0.93c?

[iaberrant]

Homework Statement

On a Starship, which travels at 0.93c, dinner is served between 8:15pm and 8:45pm, according to the clock on the ship. How long is dinner served according to stationary observes on Earth watching the ship on a video monitor?

Homework Equations

I believe the equation for time dilation to be

t'= t √ 1 - v^2/ c^2

I am sure as i do not fully understand time dilation

The Attempt at a Solution

t'= t √ 1 - v^2/ c^2

t' = 8:15 pm
v=0.93c
c=300 m/s

is this correct so far?
i need help continuing on with solving the question

Thankyou!

 

[Doc Al]

Remember that moving clocks are observed to run slow. According to Earth observers, the spaceship's clocks are moving. How much time elapses according to the moving clock? What does the time dilation formula tell you about the time according to Earth clocks?

 

[iaberrant]

ok so would that mean that that t would be the time in the spaceship ? 30 minutes which converts to 1800 seconds?
then velocity is simply 0.93c and substituting these values into the equation we get:
t'= t / (√ 1 - v^2/ c^2)
t'= 1800 / [√ 1 - (0.93c^2)^2/ c^2]
t'= 1800 / [√ 1 - 0.93c^2]
t'=4897.166056 seconds
and converted to minutes is 81.61 minutes?

is this correct?

thank you soo much for your help !~

 

[Doc Al]

Looks good! You don't really have to convert to seconds, but no harm done.

The Lorentz factor (λ) = 2.72, so the observed time is 2.72 X 30 minutes.

 

[iaberrant]

thankyou!

also how do you calculate the lorentz factor ?

 

[Matterwave]

It's just 1/sqrt(1-v^2/c^2)

 

[Doc Al]

also how do you calculate the lorentz factor ?

The "Lorentz factor" is just a name for that factor that appears in many relativistic equations; it's also called "gamma" or γ. (See Matterwave's post.) You've been calculating it all along.