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A spaceship of triangular shape, having a length three times its width, is capable of relativistic...

A spaceship of triangular shape, having a length three times its width, is capable of relativistic speeds. How fast would it have to move so that to a stationary observer its length would equal its width?

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Expert Solution

The theory of special relativity suggests that the length of a moving object seems contracted for a stationary observer. The relation between proper length i.e. length of an object in rest frame and contracted length i.e. length of object in motion with respect to stationary observer is given as,

where

L is contracted length

is proper length

v is velocity of object

c is speed of light

In the given problem, if length is to equal the width then the length has to be contracted to one-third of its proper length (since length is three times the width).

Let the proper length of spaceship be

then

using the above formula for length contraction,

where v is velocity of spaceship

cancel from both sides and solve for v to get,

squaring both sides to get,

taking square root of both side,

the spaceship would have to move at speed 0.94c so that to a stationary observer its length would equal its width.

genius_generous answered 4 months ago
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