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

The value is
`v = 0.8587 c`

Step-by-step 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 - (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 - (v^2)/(c^2) } }`

=>
`1 - (v^2)/(c^2) = [(T_1)/(T)] ^2`

=>
`1 - (v^2)/(c^2) = [(4.1)/(8)]^2`

=>
`v = 0.8587 c`