# A meterstick in a spaceship flying at one-half the speed of light would appear to be how long?

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### 1 Answer

The length of any object will appear smaller as its velocity increases according to the famous Length Contraction effect. This is esp. observed for objects moving at velocities close to that of light (c).

According to the principle of light contraction, the observed or contracted length, L, is related to original length, Lo, velocity of object, v, and speed of light, c, by the following relation:

L = L0 `sqrt(1-v^2/c^2)`

In the present case, L0 = 1m, v = 0.5 c

Thus, L = (1 m). `sqrt (1-0.5^2/1^2)`

or, L = 0.866 m.

That is to say that to a stationary observer the length of the meterstick has shrunk by 0.134 m or 13.4%.

Remember though that the length is the same for an observer abroad the ship. The contraction takes place only with regard to to a stationary observer.

Good luck.