Basic question on length contraction.

[pc2-brazil]

good night,

this is not actually a homework question, this is just plain curiosity.
we've written a basic problem on length contraction and tried to resolve it ourselves. we just want to know if the concept of the problem is right.

Homework Statement

a body of length $$L=20m$$ travels from the Earth to the Moon at a speed $$\vec{v}=0.8c$$.
find the apparent length contraction of the body seen from an observer who is at rest in relation to the Earth.
known data: distance from the Earth to the Moon: approx. 480000 km.

Homework Equations

Lorentz's length contraction: $$L'=L\gamma^{-1}$$, where $$\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$.

The Attempt at a Solution

first of all:
c = 300000 km/s;
20m = 0.02 km.
substituting the variables in Lorentz's length contraction,
$$L'=L\sqrt{1-\frac{v^{2}}{c^{2}}}$$
$$L'=0.02\sqrt{1- \frac{(0.8c)^{2}}{c^{2}} } = 0.02\sqrt{1-(0.8)^{2}}$$
$$L'=0.02\sqrt{1-0.64}=0.02\sqrt{0.36}=0.012km$$
$$L'=12m$$
therefore, the apparent length of the body will be 12 meters.

are the concept and calculations right?

 

[Doc Al]

Looks good to me.

 

[pc2-brazil]

Looks good to me.

very good, thank you for the confirmation.