Question

A) A spaceship passes you at a speed of 0.800c. You measure its length to be 31.2 m .How long would it be when at rest?
B) You travel to a star 145 light-years from Earth at a speed of 2.90

Answer 1

Answer:

a

     $l_o  =52 \  m$

b

      $l = 37.13 \ LY$

Explanation:

From the question we are told that

    The  speed of the spaceship is  $v  =  0.800c$

    Here  c is the speed of light with value  $c =  3.0*10^{8} \ m/s$

    The  length is  $l = 31.2 \  m$

     The  distance of the star for earth is $d = 145 \  light \  years$

     The  speed is $v_s = 2.90 *10^{8}$

     

Generally the from the length contraction equation we have that

       $l  =  l_o  \sqrt{1 -[\frac{v}{c } ]}$

Now the when at rest the length is  $l_o$

So  

      $l_o =\frac{l}{\sqrt{ 1 - \frac{v^2}{c^2 } } }$

      $l_o =\frac{ 31.2 }{ \sqrt{1 - \frac{(0.800c ) ^2}{c^2} } }$

      $l_o=52 \  m$

Considering b  

  Applying above equation

            $l  =l_o \sqrt{1 -  [\frac{v}{c } ]}$

Here $l_o  =145 \  LY(light \ years )$

So

           $l=145 *  \sqrt{1 -  \frac{v_s^2}{c^2 } }$

            $l =145 *  \sqrt{ 1 - \frac{2.9 *10^{8}}{3.0*10^{8}} }$

            $l = 37.13 \ LY$