Question

A spaceship carrying a light clock moves at a speed of 0.96c relative to an observer on Earth. Relative to a frame of reference that is fixed with respect to the earth, how long does it take the clock to advance 1 s?

Answer 1

Answer:

$t_o=3.5714\ seconds$

Explanation:

Given:

Speed of spaceship, v = 0.96c

using the time dilation formula, we have

$t = \frac{t_o}{\sqrt(1-\frac{v^2}{c^2})}$

where,

t₀ = time in observer's frame

t = time in observed frame

c = speed of light

substituting the values in the above equation, we get

$t = \frac{t_o}{\sqrt{1-\frac{(0.96c)^2}{c^2}}}$

or

$t = \frac{t_o}{\sqrt{1-(0.96)^2}}$

or

$t = \frac{t_o}{0.28}$

now, it is given that t = 1s  advance

thus,

$1 = \frac{t_o}{0.28}$

or

$t_o=3.5714\ seconds$