How long does it take for light to reach Earth in a moving rocket ship?

[justinh8]

Physics Relativity Question?

Homework Statement

A rocket ship is moving directly toward Earth with a constant speed of 0.50 c relative to Earth. It turns on its headlight, and the light beam travels toward Earth with speed c relative to the ship. According to the rocketship astronauts, Earth is 6.00 x 10^12 m away when the headlight is turned on. In the frame of the astronauts, how long does it take for the light to reach Earth? (Hint: in the frame of the astronauts, Earth is approaching the ship with a speed of 0.5c)

Homework Equations

c = 3x10^8 m/s

The Attempt at a Solution

I just got 20000 seconds but i know its wrong

 

[Bread18]

Can you show your working?

 

[DaveC426913]

He divided 6x10¹² by 3x10⁸. I think even justinh8 knows that doesn't qualify as "an attempt at a solution".

justinh8, you haven't been following along in class. Read the appropriate chapter in your textbook on length contraction and Lorentzian Transform.

 

[Bread18]

You need to take into account time dilation.

 

[justinh8]

There was no lesson for this, it was just a do you remember from grade 11 physics but i do not recall any lorentzian transformations in grade 11. Plus we haven't gotten our textbooks yet so i have no clue. However, i think i know one equation that might be relevant. Its ct^2 = vt^2 + ct^2. Its from grade 11 but not sure if it would work...

 

[Bread18]

There was no lesson for this, it was just a do you remember from grade 11 physics but i do not recall any lorentzian transformations in grade 11. Plus we haven't gotten our textbooks yet so i have no clue. However, i think i know one equation that might be relevant. Its ct^2 = vt^2 + ct^2. Its from grade 11 but not sure if it would work...

Hmm that's odd then. Well the equation to use is $$t=\frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}, \text{Where } t'= \text{dilated time and } t = \text{stationary time}$$

 

[SammyS]

You need to take into account time dilation.

I'm pretty sure he doesn't need to be concerned about time dilation.

Everything is given and asked in the frame of the rocket ship.

 

[Bread18]

I'm pretty sure he doesn't need to be concerned about time dilation.

Everything is given and asked in the frame of the rocket ship.

I think you're right, my mistake.

 

[Thundagere]

In which case, I think all he has to take into account is relative motions.

 

[justinh8]

I just talked to my teacher today and he said there is nothing to do with time dilation, he just said think simple so i think it might be using just the v= d/t and just rearrange it to find time??