Relative Time Dilation and Aging in Space Travel

[disneygirl828]

Homework Statement

I have a twin brother, and we're 30 years old. If i travel for three years at 2.55 X 10^8m/s (0.85c) while my brother is a rest on Earth, how much older than me will my brother be upon my return?

Homework Equations

t=To/√1-v^2/c^2

3. Try to work out
To=3
T=?
V= 2.55 X 10^8 m/s
C= (.85c) 2.55 X 10^8 m/s
T= 3/ (all of this under a square root sign -->)1-(2.55 x 10^8)^2/(2.55 x 10^8)^2
t=3/0
*i get stuck here because you can't have a zero in the denominator*

 

[BruceW]

T= 3/ (all of this under a square root sign -->)1-(2.55 x 10^8)^2/(2.55 x 10^8)^2
t=3/0
*i get stuck here because you can't have a zero in the denominator*

Hmm, you've done:
$$T= \frac{3}{\sqrt{1- \frac{v^2}{v^2}}}$$
I'm guessing you've accidentally done this?

 

[disneygirl828]

Hmm, you've done:
$$T= \frac{3}{\sqrt{1- \frac{v^2}{v^2}}}$$
I'm guessing you've accidentally done this?

Yes i used that equation, should I have used something different? If so what?

 

[BruceW]

t=To/√1-v^2/c^2

This was the right one, i.e. :
$$\frac{3}{\sqrt{1- \frac{v^2}{c^2}}}$$
c is the speed of light, but you used v instead, which is why the denominator came out as zero.

 

[BetoG93]

C = 3 x 10^8 m/s.
Remember this: the difference in ages will be the difference in the proper time and dilated time.