Question

A spaceship is moving at 0.3 times the speed of light relative to the earth. If the spaceship has a length of 15 meters, How long will it appear when observed from the earth?
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Answer 1

Answer:

The length of the object when observed from the earth appear to be 14.25m.

Explanation:

Length contraction:  

• Length contraction is a relative phenomenon, where the length of a moving object measured will be shorter than its proper length, $L_0$.
• The length contraction formula is given by

         $L=L_0\sqrt{1-\dfrac{v^{2} }{c^{2} } }$

• where $L_0$ is the proper length that refers to the length measured by an observer in rest frame.
• $L$ is the length measured by an observer in moving frame,
• $v$ is the speed of the object and $c$ is the speed of light in vacuum.

Given the spaceship is moving with 0.3 times the speed of light relative to the earth, i.e., $v=0.3c$

Length of the spaceship, $L_0= 15 m$

Substituting the given values in the formula of length contraction,

$L=15\sqrt{1-\dfrac{(0.3c)^{2} }{c^{2} } }$

  $=15\sqrt{1-\dfrac{(0.3)c^{2} }{c^{2} } }$

 $=15\sqrt{1-0.09 }=15\sqrt{0.91 }$

 $=15\times 0.95\approx14.25m$

Therefore, the length of the object when observed from the earth appear to be 14.25m.

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