Question

Imagine you are on a spaceship. A second spaceship rockets past yours at 0.5 cc. You start a stopwatch and stop it 10 seconds later. For an astronaut in the other spaceship, the number of seconds that have ticked by during the 10 seconds on your stopwatch is____________

Answer 1

`t=11.547\,s`

Step-by-step explanation:

Given is the case of time dilation where the velocity of other spaceship is comparable to the velocity of light, i.e. relativistic velocity.

Given that:

velocity of the fast moving spaceship,
`v=(0.5* c)\,\,m.s^(-1)`

where c is the velocity of light.

times according to the other spaceship, (relativistic time)
`t'=10\,s`

For time dilation we have the equation as:

`t'=t \sqrt{1-(v^2)/(c^2) }`

`\Rightarrow 10= t \sqrt{1-((0.5c)^2)/((c)^2) }`

`t=11.547\,s`