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

Answer:

0.407 c

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

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

Inserting the values

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

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

v = 0.407 c