Question

The Millennium Falcon was constructed 43.6 m long. a) How fast is it traveling past Luke when he measures its length to be 30.1 m. b) At this speed, what is the Falcon's length as measured by Han Solo who is traveling in the Falcon.

Answer 1

Answer:

a)0.5564c

b)43.6 m

Explanation:

Given proper length of falcrum L₀= 43.6 m

improper length L=30.1 m (when viewed from moving frame)

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

$30.1=43.6\sqrt{1-\frac{v^2}{c^2}$

⇒$\{1-\frac{v^2}{c^2}}$=$\frac{30.1}{43.6}$

${1-\frac{v^2}{c^2}}=0.6904$

$\frac{v^2}{c^2}=0.3096$

$v^{2}=3096c^{2}$

v=0.5564c

this is the required speed of falcon when it passes luke

b). Since Han solo is on the Falcon its reference frame will be falcon itself hence there wont be any change in the length of Falcon that its length will be

43.6 m