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

The speed of Lilac is 0.399c.

Step-by-step 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-(v^(2))/(c^(2))} \\`

`1-(v^(2))/(c^(2)) = \left ( (L)/(L_(0)) \right )^(2) \\`

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

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

`v = 0.399c`