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

Answer:

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

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 :

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

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