A pair of twins live in (city). one drives around the world in his fast blue car, leaving the city in a fixed direction with a constant velocity v. The proper circumference of the Earth is 2PiR - ignore the rotation of the earth.
1 -What is the age difference between the two twins when they meet again??
Also, have an optional question - no marks for this, but would be interested in hearing any ideas:
2 -The twin who stayed in the city looks at the car of his brother - does the colour of the car change during the journey? how?
I would say yes, but not sure if it's due to length contraction i.e of wavelengths of the light that hit the car at different points around the world (i.e differing frames of reference), hence fading the paint - may be wrong, but like I said, no marks for it anyway
The Attempt at a Solution
At the moment I have the time dilation equation
dt= t2-t1 = Tau/ sqrt(1-(v^2/C^2)
My main problem is that I can find values for the length of the journey (ie circumference of Earth and speed of light is easy enough) but how do I calculate the velocity travelled?
I know that v=s/t (but I'm trying to work out t anyway)
Starting to think it may be a question that doesn't require a numerical answer