Question

How fast must an object be going if its rest length is 3.4 times as long as its observed length?

Answer 1

The formula for observed length is given by:

Observed length = (Length at rest)*{1-(v/c)²}^1/2

Now, Length at rest = 3.4*Observed Length

Therefore, 1 = 3.4*{1-(v/c)²}^1/2

1 = 11.56*{1-(v/c)²}

{1-(v/c)²} = 1/11.56 = 0.0865

(v/c)² = 0.9135

v/c = 0.956

v = 0.956*c = 0.956 * 3 * 10⁸ m/s

v = 2.87*10⁸ m/s

Therefore, the object must be moving at 2.87*10⁸ m/s.

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