Question

The spaceship Lilac, based on the Purple Planet, is 759 m 759 m long, as measured at rest. When Lilac passes Earth, observers there measure its length to be 688 m 688 m . At what fraction of the speed of light is Lilac moving with respect to Earth?

Answer 1

The speed of Lilac is 0.422 times of the speed of light.

Step-by-step explanation:

Given that,

Length of the spaceship Lilac at rest,
`L_o=759\ m`

When Lilac passes Earth, observers there measure its length to be 688 m, L = 688 m

We need to find the speed of light is Lilac moving with respect to Earth. The formula of length contraction is given by :

`L=L_o\sqrt{1-(v^2)/(c^2)} \\\\(v)/(c)=\sqrt{1-((L)/(L_o))^2} \\\\(v)/(c)=\sqrt{1-((688)/(759))^2} \\\\(v)/(c)=0.422\\\\v=0.422c`

So, the speed of Lilac is 0.422 times of the speed of light.