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

a

`l_o  =52 \  m`

b

`l = 37.13 \ LY`

Step-by-step 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 -[(v)/(c ) ]}`

Now the when at rest the length is
`l_o`

So

`l_o =\frac{l}{\sqrt{ 1 - (v^2)/(c^2 ) } }`

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

`l_o=52 \  m`

Considering b

Applying above equation

`l  =l_o \sqrt{1 -  [(v)/(c ) ]}`

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

So

`l=145 *  \sqrt{1 -  (v_s^2)/(c^2 ) }`

`l =145 *  \sqrt{ 1 - (2.9 *10^(8))/(3.0*10^(8)) }`

`l = 37.13 \ LY`