Question

A law enforcement officer in an intergalactic "police car" turns on a red flashing light and sees it generate a flash every 1.2 s. A person on earth measures that the time between flashes is 2.2 s. How fast is the "police car" moving relative to the earth?

Answer 1

Answer:

The velocity of the police car relative to earth is $v_{rel} = 2.51\times 10^{8} m/s$

Given:

time for flash generation of the inter galactic police car, t = 1.2 s

time between flashes as measured from earth, t' = 2.2 s

Solution:

Utilising Einstein's equation for time dilation to calculate the velocity of the police car, the equation is given by:

$t' = \frac{t}{\sqrt {1 - \frac{v^{2}}{c^{2}}}}$                                (1)

where, c = speed of light in vacuum = $c = 3\times 10^{8}$

re arranging eqn (1) for velocity, v:

$v_{rel} = c\times \sqrt {1 - (\frac{t}{t'})^{2}}$                               (2)

Now, from eqn (2)

$v_{rel} = 3\times 10^{8}( \sqrt {1 - (\frac{1.2}{2.2})^{2}})$

$v_{rel} = 3\times 10^{8}\times 0.838$

$v_{rel} = 2.51\times 10^{8} m/s$