Question

The spaceship Lilac, based on the Purple Planet, is 717 m717 m long, as measured at rest. When Lilac passes Earth, observers there measure its length to be 655 m655 m . At what fraction of the speed of light is Lilac moving with respect to Earth?

Answer 1

0.407 c

Step-by-step explanation:

L₀ = Actual length of the spaceship lilac = 717 m

L = length of spaceship observed = 655 m

v = speed of lilac relative to earth

Using the equation

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

Inserting the values

`655 = 717\sqrt{1 - \left ( (v)/(c) \right )^(2)}`

`0.9135 = \sqrt{1 - \left ( (v)/(c) \right )^(2)}`

v = 0.407 c