Question

Aliens slowing down to observe Earth often are distracted by lighthouses. As aliens pass Earth in their spaceship they notice a lighthouse completes its circuit once every 8.0 s, however the lighthouse attendant has set the lighthouse to complete its circuit every 4.1 s from his point of view. How fast is the alien spaceship traveling in terms of the speed of light?

Answer 1

Answer:

The value is $v = 0.8587 c$

Explanation:

From the question we are told that

The time taken as seen by aliens $T = 8.0 \ s$

The time taken as seen by attendant $T_1 = 4.1 \ s$

Generally from the dilation of time equation we have that

$T = \frac{T_1}{ \sqrt{ 1 - \frac{v^2}{c^2} } }$

Here c is the speed of light

v is the speed of the alien ship

=> $8 = \frac{4.1}{ \sqrt{ 1 - \frac{v^2}{c^2} } }$

=> $1 - \frac{v^2}{c^2} = [\frac{T_1}{T}] ^2$

=> $1 - \frac{v^2}{c^2} = [\frac{4.1}{8}]^2$

=> $v = 0.8587 c$