Time dilation problem

by spXq
Tags: dilation, time
 P: 4 The distance to Alpha Centauri is 4,3 light years. How fast would a space ship have to travel to get there in 10 years, according to the crew? The answer *should* be 0,395c. So far I've gotten all sorts of answers but not much close, so I seem to be approaching the problem the wrong way.
 Mentor P: 40,689 Show what you've done so far. Hints: What's the basic idea of time dilation? What's the definition of velocity?
 P: 4 The first part of the assignment asks for the time required when traveling at 30% of light speed. Given a gamma factor of 1,048 I get ~13,7 years, which is correct (so the gamma factor must be correct as well). velocity = distance / time But... for t = 10 and d = 4,3 v = 4,3 / 10 v = 0,43, which is wrong taking length contraction into account gives 4,3/1,048 = 4,1 v = 4,1 / 10 v = 0,41, which is still wrong
Mentor
P: 40,689

Time dilation problem

 Quote by spXq Edit: velocity = distance / time
Good. Keep going.

From Earth's viewpoint, you have the distance. What's the time?
P: 4
 Quote by Doc Al Good. Keep going. From Earth's viewpoint, you have the distance. What's the time?
Hmm... i don't know. :/

The distance is 4,3 ly but I don't know the speed, so how do I find the time?
 P: 4 Hang on... the time for the crew is 10 years so the time for the observer is t/gamma 10/1,048 = 9,54 years Edit: no that's not right....... I have no idea what I'm doing Edit2: the time from earths viewpoint is d * gamma = 4,3 * 1,048 = 10,48 years, while the time is 10 years for the crew
Mentor
P: 40,689
 Quote by spXq Hang on... the time for the crew is 10 years so the time for the observer is t/gamma
You have that reversed. If the ship time is 10 years, then to earth observers it will be longer: t*gamma, not t/gamma.

 10/1,048 = 9,54 years
In addition to what I already pointed out, do not use the gamma from the previous part of the question.

So continue with that velocity equation, v = d/tearth.

 Related Discussions Introductory Physics Homework 4 Special & General Relativity 14 Advanced Physics Homework 2 Introductory Physics Homework 0 Special & General Relativity 4