## Homework Statement

Two rockets are sent off at t=0, one from x=0 and the other at x=4. The rocket leaving from x=0 is moving at .8c and the rocket leaving x=4 is moving at .2c. When the paths of the two rockets meet, they send a light signal to x=0. Read off the coordinates in the S frame and in the S' frame and check to see that the space and time differences between events 3 and 4 satisfy the invariant rule. Event 3 is the light signal being sent out and event 4 is the light signal arriving at x=0.

The S' frame is moving at .6c.

## Homework Equations

x' = $$\gamma$$(x-vt)

t' = $$\gamma$$(t - vx/c^2)

invariant rule: (t4 - t3)^2 - (x4 - x3)^2 = (t'4 - t'3)^2 - (x'4 - x'3)^2

## The Attempt at a Solution

So after drawing all world lines, I came up with the coordinates (3.5, 2.75) for event 3 and (0, 6.3) for event 4 in the S frame by looking at the graph. I am confident in these coordinates.

In the S' frame, I came up with (2.8, 1.1) for event 3 and (-6, 9.8) for event 4 in the S' frame. This is where I think there may be a mistake. These are just based off reading the graph, so they are approximate.

Now when I check to see if it satisfies the invariant rule,

(6.3-2.75)^2 - (0-3.5)^2 = (9.8-1.1)^2 - (-6 - 2.8)^2

.3525 = -1.75

Clearly this is not correct. I understand there will be some error since I am just eyeballing the coordinates from the graph, but this seems way off. Does anybody see where I went wrong?

vela
Staff Emeritus
Homework Helper
What units are you using? In what direction do the spaceships move? Are the coordinates you're giving (x,t) or (t,x)?

Each of the spaceships are moving towards each other. So the ship that launches from x=0 is moving towards x=4 and vice versa. I am giving the coordinates as (x,t).

vela
Staff Emeritus