Question

An astronaut, whose height on the earth is exactly 6 ft is lying parallel to the axis of a spacecraft moving at 0.800c relative to the earth. Calculate the height as measured by an on the earth and by an observer on the same same spacecraft.

Answer 1

For an observer on the Earth height will be calculated by the equation:

$L = L_0\sqrt{1 - \frac{v^2}{c^2}}$

$L = 6\sqrt{1 – 0.64}$

$L = 3.6\;ft$

An observer in the same spacecraft will measure the height to be 6 ft, since there is not relative motion between the observer and the astronaut (v = 0 in the above equation).