# Finding the time it takes a light source to hit an observer

#### PatrickSta

The question I am trying to solve is:

In A frame, a light source at rest located at x = 0 emits a pulse P_1 at t_1 = 0, emits another pulse P_2 at t_2 = t. A’ frame moves with constant speed V along X axis with A frame. Observer in A’ at X’ = 0 receives P_1 at t_1’ = 0, X_1’ = 0 (i.e. P_1 was emitted when the origin of A and A’ were exactly at the same location). Find t’ when observer at X’ = 0 receives P2 in the A’ frame.

I know that it has to do with special relativity and time dilation but I don't know where to start and am confused on how to solve it.

#### HallsofIvy

How long it takes a light source to hit an observer? That depends upon how fast you throw it!

You say that the two frames are at exactly the same point at time 0 and that A' is moving with speed V (relative to frame A) so at the time t A' is distance Vt from frame A. The whole point of relativity is that light has the same speed in any frame. In frame A', the observer is stationary while the light travels distance Vt at speed c. It will take Vt/c for the light to reach observer A'

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#### Pmb

PHF Hall of Fame
The question I am trying to solve is:

In A frame, a light source at rest located at x = 0 emits a pulse P_1 at t_1 = 0, emits another pulse P_2 at t_2 = t. A’ frame moves with constant speed V along X axis with A frame. Observer in A’ at X’ = 0 receives P_1 at t_1’ = 0, X_1’ = 0 (i.e. P_1 was emitted when the origin of A and A’ were exactly at the same location). Find t’ when observer at X’ = 0 receives P2 in the A’ frame.

I know that it has to do with special relativity and time dilation but I don't know where to start and am confused on how to solve it.
This sounds like a homework problem. In any case it is the policy if this forum that people show an attempt to solve the problem themselves.

By the way. It is not the whole point of relativity is that light has the same speed in any frame. That's only have the point. The other half is that the laws of physics are the same in all frames of reference.