Question

In a Star Track video scene, Spock stands on a space platform of length 65 m. A rocket passes by at 0.8c parallel with the edge of the platform. Spock jotted down in his notes that there is an instance where the front and back of the rockets are aligned simultaneously with the ends of the platform as in Figure 1.
Determine
(i) according to Spock, the time rocket passes by a position on the platform.
(ii) according to Chan in the rocket, the length of the platform.

(iii) according to Chan in the rocket, the time Spock takes to move a distance similar to the length of his rocket.

(

Answer 1

question i)
the requested time \(t_S\), in the spock reference system is:
\[{t_S} = \frac{L}{v} = \frac{{65}}{{0.8c}} = ...?\]

Answer 2

whereas the requested time \(t_R\) in rocket reference system is:
\[{t_R} = \frac{{{t_S}}}{\gamma }\]
where, as usual:
\[\gamma = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\]