The premise of the Planet of the Apes movies and book is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth’s future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again.

Question

anonymous · Answer

O_O    you know ur in mathematics correct?

ganeshie8 · Answer

Yes, this is applied math haha!
familiar with special relativity ?

anonymous · Answer

derp    O_o       nope.      7th grade advanced, just learning it.

ganeshie8 · Answer

Ahh its not hard, do you want to learn some ?

anonymous · Answer

sure, im gonna have to use it sooner or latter.

ganeshie8 · Answer

Awesome! To start with let me ask you a small question

ganeshie8 · Answer

Imagine you're in a train that is going at `60 miles per hour` relative to the ground.

ganeshie8 · Answer

What is your velocity relative to the train ?

xmissalycatx · Answer

$$x _{1^{2}}+x _{2^{2}}=t^2$$

anonymous · Answer

well, which direction am i going? i got everything i know so far from here http://www.mathsisfun.com/measure/us-standard-speed.html and it says velocity is the speed your going in a direction *Example* 60 mp5 westward

anonymous · Answer

*mph westward

ganeshie8 · Answer

That is correct! but your velocity relative to the train is ZERO because you're sitting in the train. The train is not going anywhere from you. watch this awesome video when free :) https://www.youtube.com/watch?v=ev9zrt__lec

anonymous · Answer

well, thanks.  this actually helped me alote, i have a brother in the 9th grade learning this, and it will be fun to help him with his work, and watch his face.   this is my best subject, and i love to learn more about it. again, thanks

ganeshie8 · Answer

lol that sounds fun, but you're gonna love special relativity once you get a taste of it! good luck !

anonymous · Answer

Thanks!! :)

error1603 · Answer

Thanks!

samigupta8 · Answer

I think it should be just twice the ditsance that they  travelled in  one go.

samigupta8 · Answer

But i m of firm opinion that it should be something else..
Bcoz u have asked a question then that won't be as easy as that.
:)

ganeshie8 · Answer

are you saying they will land back on earth after 240 years (as measured on earth frame) ?
 @samigupta8

samigupta8 · Answer

No they will land back on earth in 120 years ..
60 yrs for going outward and 60 for return journey.

ganeshie8 · Answer

Oh right, right!
 that is correct if Newtonian physics is correct

samigupta8 · Answer

No they will land back on earth in 120 years ..
60 yrs for going outward and 60 for return journey.

ganeshie8 · Answer

But the answer given is 2684 years !

samigupta8 · Answer

U asked the distance .
Right?
Are u telling the ans in units of light years?

samigupta8 · Answer

It will make the same c*y is same as light year!

ganeshie8 · Answer

`how far into Earth’s future`

it is asking time i guess...

samigupta8 · Answer

What's the use of relative speed then ?

ganeshie8 · Answer

the faster the relative sped, the more you go into the "future"

ganeshie8 · Answer

do you watch movies ?

samigupta8 · Answer

I meant the numerical purpose of it.

ganeshie8 · Answer

Let $\Delta t_0$ be the time taken for the roundtrip in astronauts starship frame

ganeshie8 · Answer

What can you say about the time taken for the roundtrip in Earth's frame ?

ganeshie8 · Answer

ahh you should watch english movies too sometimes

samigupta8 · Answer

∆to - t