The Enterprise and the Klingon Battle Cruiser - Solution
Captain Kirk is correct and Dr. McCoy is wrong.
The front end of the Battle Cruiser will pass by
the rear end of the Enterprise at point C. In the Klingon frame, this
is simultaneous with E so that is the space-time point at which the
disruptor cannon will be fired. The front end of the Enterprise is at
F in the Klingon frame so they will miss. In the enterprise frame, E
is simultaneous with H so the front end of the Battle Cruiser will
not have reached the rear end of the Enterprise yet. So even though
the Battle Cruiser will be shorter due to Lorentz contraction in the
Enterprise frame, they will still miss.
McCoy : Damn it Spock! I'm a doctor. Not a Vulcan physicist!
Back to problem
Spock : Doctor, you should have gone to Virgina Tech when you were
still a pre-med student back on Earth. They have an excellent course on
relativity which has been part of their core curriculum since the 20th century!