Special Relativity spacetime intervals HW help

[Nivek43]

Homework Statement

The Tale:
The Klingon home world of Kronos is located at x=0. At time ct=-4 , a wonderful event occurs: Federation emissaries negotiate a peace treatywith the Klingons, bringing many years of warfare to an end! As part of this treaty, the Federation agrees to share its vast research database with the Klingons. As soon as the peace treaty is signed (x=0, ct=-4), the Fed. negotiators board their ship and set out from Kronos in the +x direction at speed .6c.

Armed with new knowledge, the Klingon scientists get to work...and before long, they are on the verge of a profound discovery: with a clever modification of their warp drive, they can make a faster-than-light warship! At time ct=0, the scientist K'pril solves the final piece of the puzzle: he solders the essential wire in place of the great warship Kahless, and the Klingon High council immediately launches the Kahless from Kronos. THe newly modified warship races off at velocity 3c in the +x direction, intent on destruction.

The Klingon high command chuckles with glee when their observers report the first success of the Kahless: the complete destruction of a Federation outpost at position x=+1.

The Kahless continues on its way without any change in course... and because of its tremendous speed, it soon catches up with the Fed. negotiators! The dreadful warship instantly powers weapon, and vaporizes the negotiators' ship.

The story above describes 4 events (underlined), some of which involeve a ship traveling faster than light-speed.

1. Plot the four events as seen by the scientists on Kronos and the world-lines for Kronos, Fed. neg., and Kahless.

2. Then plot the four events and world-lines in the frame of the fed. negotiators.

Homework Equations

I=(ct)^2-x^2-y^2-z^2
Lorentz Transformations.

The Attempt at a Solution

Now I think I can plot the first 3 events for the first part. I'm just having trouble with calculating the destruction of the negotiators. I tried doing something with spacetime intervals I=(ct)^2-x^2-y^2-z^2 but I can't seem to be getting anywhere. If someone could provide some hints that would be wonderful.

 

[Doc Al]

I'm just having trouble with calculating the destruction of the negotiators.

When the Kahless takes off, where is the Federation ship? How long does it take for the Kahless to overtake the other ship? What time and place does that happen? (Use Kronos coordinates to start with.)

 

[Nivek43]

I think I may have gotten the first part, but I'm feeling uncertain. I did t'=5/4(4-0)=5 and then x'=5/4(0-.6*4)=-3. This doesn't make sense to me, I used the lorentz transformations with t' and x' being in the reference frame of the Negotiators. And then x=0 because the people on Kronos see the two events happen at the same position and then used t=4 because the duration between the two events in the scientists' eyes is 4. But that negative length is screwing me up.