Question on Special Relativity (1 Viewer)

[Vizsla]

Could one of you please help me with this question and explain how the two answers differ.

 

[rand_althor]

a) An observer on Earth would see the rocket travel the normal distance, in a dilated time period. You would calculate the time taken to complete the journey using v=d/t. And then use the time dilation formula to calculate the dilated time.

b) An astronaut on the rocket would see the path of the rocket to be contracted, and would record the time taken to be normal. You would calculate the contracted length, and then use v=d/t to determine the time taken.

 

[porcupinetree]

View attachment 32207

Could one of you please help me with this question and explain how the two answers differ.

The times should be equal. However, if we were hypothetically talking about someone on earth observing the rocket, or vice versa, time would appear to run slower in the observed frame of reference

 

[MaccaFacta]

This is a lot more complicated that it looks... a rocket travelling at 0.75 c will take 9 / 0.75 = 12 years to travel the distance. But let's pretend that someone on the "distant planet" shines a green light towards Earth when the rocket arrives - then that signal would take 9 years to get from there to here. So the observer on Earth would wait 21 years for confirmation that the rocket had arrived! An astronaut in the rocket will observe length contraction of the distance between Earth and the distant planet, so the distance from Earth to the distant planet in the astronaut's reference frame is 5.95 light years. So the trip will take 7.93 years from the astronaut's reference frame.

 

[PhysicsMaths]

This is a lot more complicated that it looks... a rocket travelling at 0.75 c will take 9 / 0.75 = 12 years to travel the distance. But let's pretend that someone on the "distant planet" shines a green light towards Earth when the rocket arrives - then that signal would take 9 years to get from there to here. So the observer on Earth would wait 21 years for confirmation that the rocket had arrived! An astronaut in the rocket will observe length contraction of the distance between Earth and the distant planet, so the distance from Earth to the distant planet in the astronaut's reference frame is 5.95 light years. So the trip will take 7.93 years from the astronaut's reference frame.

Your answer is correct but it seems you're over complicating things a bit
All that's required is substituting 12 into the time dilation equation