|College of Science Physics Dept Tatsu Takeuchi Special Relativity Practice Problems|
The Enterprise and the Klingon Battle Cruiser
A Klingon Battle Cruiser is equiped with a disruptor cannon mounted on its rear end which can only fire perpendicularly to its direction of motion. A standard Klingon tactic is to fly by its enemy and fire this cannon as the front end of the Battle Cruiser passes the enemy ship's rear end. In the following discussion, assume that the Battle Cruiser flies by so closely that you can neglect the time it takes for the disruptor beam to travel from the cannon to the target.
The Starship Enterprise, which is the same length as the Battle Cruiser when both are at rest, is about to be attacked. Dr. McCoy is worried that, due to Lorentz contraction, the Klingon Battle Cruiser will be shorter than the Enterprise and therefore cannot miss. Captain Kirk, on the other hand, claims that the Enterprise will be shorter than the Battle Cruiser when seen from the Klingons' frame so that there is nothing to worry about.
McCoy : Damn it Jim! We're the ones getting shot at. It's our frame of reference that matters!
You, Mr. Spock, must calmly draw a space-time diagram and explain to them which of them is right.
Spock : Doctor, I assure you that I am doing the best I can under the circumstance.
Answer the following questions: