physics question: The Relativity of Length: Length Contraction?

Question

A woman and a man are on separate rockets, which are flying parallel to each other and have a relative speed of 0.900c. The woman measures the same value for the length of her own rocket and for the length of the man's rocket. What is the ratio of the value that the man measures for the length of his own rocket to the value he measures for the length of the woman's rocket?


his rocket / woman's rocket =

Answer 1

Good question.

First, some equations:
gamma = 1/(1-sqrt[1-{v^2/c^2}]) v = rel. vel. c = speed of light

L1 = Lo/gamma --> this is length contraction.

w=woman
m=man

The woman sees the length as equal, so L1w = Lom which means gamma = 1.

Next, what does the man see? He sees
L1m = Low/gamma but now we calculate gamma = 1/(1-sqrt[1-{0.9^2*c^2/c^2}]) and you will get gamma = 2.29

now, the question you asked was ratio his rocket/her rocket or in the above notation:

L1m/L1w
= (Low/gamma)/Lom
= (Low/2.29)/Lom
= Low/(2.29*Lom)

That should do it.

To the above poster, you would be correct if the problem said their absolute velocities were 0.900c, but in this case they are relative and thus change accordingly in the frames of reference.

Answer 2

If they are side by side, and there is no acceleration of either one, which would they not be the same?