Photons fired from the back of a moving spacecraft

[Morgan8i6]

Homework Statement

If a passenger at the back of a spaceship traveling at 3/5c fires a photon forward how long will it take to hit the front of the spaceship in the reference frame of the spaceship if it is 1 light second long? How long will it take in the stationary frame?

Homework Equations

T=t/(1-v^2/c^2)^1/2

The Attempt at a Solution

I completed the first half of the problem. Plugging in 1 second in for t (time it takes a photon to travel one light second) and 3/5c (the velocity of the reference frame) for v gives me 5/4 seconds. I just can't figure out what I should be inputting for the variables in the statuary reference frame. The answer sheet says a stationary observer would measure the time T to be 5/2 seconds.

 

[mfb]

I completed the first half of the problem. Plugging in 1 second in for t (time it takes a photon to travel one light second) and 3/5c (the velocity of the reference frame) for v gives me 5/4 seconds.

No, that is not correct. In the reference frame of the spaceship, the spaceship is at rest. The 3/5c relative to some arbitrary observer somewhere else are completely irrelevant.

I just can't figure out what I should be inputting for the variables in the statuary reference frame.

You can use Newtonian mechanics here, if you like, if you calculate the length of the spaceship - as seen by the observer - with relativistic mechanics first.

 

[tia89]

If a passenger at the back of a spaceship traveling at 3/5c fires a photon forward how long will it take to hit the front of the spaceship in the reference frame of the spaceship if it is 1 light second long? How long will it take in the stationary frame?

You should specify in which reference the ship is 1 light second long.

In the most natural case (1 second long is the proper length), then consider that ANY observer will see light with speed $c$.

Also consider using for the second part of the problem, the length contraction instead of the time dilatation. Meaning, compute in the lab frame which would be the length perceived of the ship, and then use light speed $c$.