Lorentz transformation and rockets

[~Sam~]

Homework Statement

1The rockets of the Goths and the Huns are each 1000 m long in their rest frames. The rockets pass each other, virtually touching, at a relative speed of 0.8c. The Huns have a laser cannon at the rear of the rocket that shoots a deadly laser beam at right angles to the motion. The captain of the Hun rocket wants to send a threatening message to the Goths by “firing a shot across their bow”. He tells his first mate, “The Gothsʼ rocket is length contracted to 600 m. Fire the laser cannon at the instant the nose of our rocket passes the tail of their rocket. The laser beam will cross 400 m in front of them.” But things are different in the Gothʼsʼ reference frame. The Goth captain muses, “The Hunsʼ rocket is length contracted to 600 m, 400 m shorter than our rocket if they fire the laser cannon as their nose passes the tail of our rocket, the lethal blast will go right through our side.”
The first mate on the Hun rocket fires as ordered. Does the laser beam blast the Goths or not? Resolve this paradox. Show that, when properly analyzed, the Goths and the Huns agree on the outcome. Your analysis should contain both quantitative calculations and written explanation.

Homework Equations

All Lorentz Transformation equations.(ie.x=(x-vt) / sqrt(1-v^2/c^2)

The Attempt at a Solution

Not sure where to start although I know I will have to do Lorentz transformations. Any ideas>

 

[tiny-tim]

Hi ~Sam~!

(have a square-root: √ and try using the X² tag just above the Reply box )

Start in the Hun frame …

let the front of the Goth rocket in that frame be at (x₀,t₀), and the rear be at (x₁,t₁) …

what happens in that frame? ​