Question

The spaceship Lilac, based on the Purple Planet, is 721 m long when measured at rest. When the Lilac passes Earth, observers there measure its length to be 661 m. At what speed v is the Lilac moving with respect to Earth? Express your answer as a multiple of the speed of light c.

Answer 1

Answer:

The speed of Lilac is 0.399c.

Explanation:

The size of spaceship Lilac measured at the rest position = 721 m  

The length of  Lilac when it passes Earth = 661 m

Below is the calculation for speed at which Lilac is moving.

Here, L, is the length of spaceship when it passes the earth.

$L_{0}$ is the length of spaceship measured at rest.

V is the speed.

$L = L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}$

$1-\frac{v^{2}}{c^{2}} = \left ( \frac{L}{L_{0}} \right )^{2}$

$\frac{v}{c} = \sqrt{1-\left ( \frac{L}{L_{0}} \right )^{2}}$

$\frac{v}{c} = \sqrt{1-\left ( \frac{661}{721} \right )^{2}}$

$v = 0.399c$