Question

How fast does a 245-m spaceship move relative to an observer who measures the ship's length to be 175m? ?c

Answer 1

from the relativity we know

$\gamma =\frac{1}{\sqrt{1-v^{2}/c^{2}}}$

given

$\gamma =\frac{245}{175}\\\\ \frac{1}{\sqrt{1-v^{2}/c^{2}}}=\frac{245}{175}\\\\ \sqrt{1-v^{2}/c^{2}}=\frac{175}{245}\\\\ 1-v^{2}/c^{2}=\left ( \frac{175}{245} \right )^{2}\\\\ v^{2}/c^{2}=1-\left ( \frac{175}{245} \right )^{2}\\\\ v^{2}/c^{2}=0.4898\\\\ v=\sqrt{0.4898}c\\\\ v=0.700c$

so the velocity of shp is0.700c in three significant figure