How fast would an object have to be travelling in order to decrease its length in half?

Question

The answer is 0.866c, but I don't understand how to get this answer. Can somebody please explain to me?

Answer 1

(sqrt 3)/2 c = 2.6 x 10^8 m/s

Here's how: L/Lo = sqrt[1 - (v/c)^2] = 1/2

So (v/c)^2 = 3/4 and the rest is easy.

Answer 2

Just use a special relativity equation:

L' / L = sqrt(1-[v/c]^2) = 0.5

Solve for V, you'll get your answer

Answer 3

If we use the Fitzgerald contraction Hypothesis, the relationship is:

L' = L( 1 - v^2/c^2) ^0.5

Where:

L = the length at rest

L' = length in motion

Thus:

(L'/L)^2 xc^2 = c^2 - v^2

0.5^2x c^2 - c^2 = -v^2

-0.75c^2 = -v^2

v = csqrt(0.75) = 0.866c