Question

An extra-galactic space fleet passes the earth with v = 0.95c, when they notice that you are on a physics mission in modern physics. It takes you 50 minutes to complete the mission.
They decide to measure the writing time and length of your test paper with a "Strompf-Zygniebwo-meter"
How long do the aliens think the mission will take? How far do they think the writing paper is (

Answer 1

Let's denote the time passed in the laboratory system on Earth with $t_0 = 50 min$. Then, according to the Lorentz transformations, the time recorded in the space fleet will be:

$$t = \dfrac{t_0}{\sqrt{1 - \dfrac{v^2}{c^2}}} = \dfrac{50min}{\sqrt{1 - \dfrac{(0.95c)^2}{c^2}}} \approx512.8 min$$

Assuming the report was written on A4 paper, and the space fleet is moving along it's big axis ($L_0 = 297mm)$ ), then the size of the report will be:

$$L = L_0\sqrt{1 - \dfrac{v^2}{c^2}} = 28.9575 mm$$

Answer. 512.8 min, 28.9575 mm.