# Special relativity homework question time dilation

Special relativity homework question time dilation
1. Homework Statement
You are a passenger on a brand-new spaceship that travels at 95% of the speed of light, i.e.,
v = 0.95 × c. The spaceship is bound for the star, Altair, at a distance of 17 light years from
Earth. If the spaceship departs on your 21st birthday, at a speed of v = 0.95c, how old are you
when the spaceship arrives at Altair?

2. Homework Equations
Δtmoving = Δtrest x [square root of (1−v^2/c^2)]

v= d/t

3. The Attempt at a Solution
I have no idea how to do this problem, in my opinion it appears to be poorly worded, I don't know if the professor means age relative to earth time or age relative to the traveling speed. This is my attempt to find a solution:

v=d/t v=0.95c --> 0.95c= 17lightyears/ t

t= d/ v

t= 17ly/ 0.95 c

Doc Al
Mentor
I have no idea how to do this problem, in my opinion it appears to be poorly worded, I don't know if the professor means age relative to earth time or age relative to the traveling speed.
They want the actual biological age of the passenger when he arrives at the destination. So it's his frame that we are interested in.

This is my attempt to find a solution:

v=d/t v=0.95c --> 0.95c= 17lightyears/ t

t= d/ v

t= 17ly/ 0.95 c
What you found is the time the trip takes according to Earth observers. That's not quite it. What would the time be according to the spaceship?

okay, I understand how to do it, so I plug what I calculated into the time dilation equation as delta t rest and calculate tmoving based on what I have given. Thank you!

Doc Al
Mentor
okay, I understand how to do it, so I plug what I calculated into the time dilation equation as delta t rest and calculate tmoving based on what I have given. Thank you!
Good! That works.

Another approach that will give you the same answer is to ask yourself: What is the distance traveled according to the spaceship? Then you can use T = D/V from the spaceship's frame.

rude man
Homework Helper
Gold Member
.. and the answer is ...?

the answer for tmoving is 5.6 and when you add that to the age of the passenger that is 21yrs+ 5.6 yrs= 26.6 yrs old when the ship arrives at Altair!