> College of Science > Physics Dept > Tatsu Takeuchi > Special Relativity > Practice Problems > Problem 9
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### The Duel of the Klingon Battle Cruisers

A Klingon Battle Cruiser is equiped with a disruptor cannon mounted on its nose which can only fire in the direction perpendicular to its direction of motion. The Cruiser is well protected by shields except for one vulnerable spot on its rear end.

Two of these Battle Cruisers challenge each other to a duel. They fly straight toward each other and fire their cannons as they pass by, trying to hit the vulnerable spot of the opponent.

The commander of Cruiser 1 thinks that she will win since, due to Lorentz contraction, her opponent's ship will be shorter than hers which will allow her cannon to fire at the opponent's vulnerable spot before the opponent gets a chance to fire his cannon at her vulnerable spot.

The commander of Cruiser 2 thinks that he will win due to the exact same reason.

The duel takes place and when observed from a frame fixed to a nearby planet, both Cruisers are the same lengths, they fire their respective cannons at the same time, and they are both hit.

The trajectories of both Cruisers are shown in the space-time diagram. The cannon of Cruiser 1 (coming in from the left) is fired at point Q, and the cannon of Cruiser 2 (coming in from the right) is fired at point P.

Answer the following questions:

1. In the frame moving with Cruiser 1 (coming in from the left), at which space-time point, labeled A through L, is the nose of Cruiser 2 (coming in from the right) when the cannon of Cruiser 1 is fired at Q?
2. In the frame moving with Cruiser 1, what is the chronological order in which the two cannons are fired?
3. When Cruiser 2 is hit by Cruiser 1's cannon at Q, a light signal is sent toward the nose of the Cruiser to inform the commander of the damage. At which space-time point does the signal reach the nose of Cruiser 2?
4. What was wrong with the commanders' reasoning that they will win? Explain, referring to the space-time diagram.