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1. The problem statement, all variables and given/known data

"A space-ship is going at its maximum velocity ##v_{max}##, and fires a missile which travels at ##v_{max}+u##. Can it ever catch up to it?"

2. Relevant equations

Let ##v_{max}## be the ship's maximum velocity.

Let ##u## be the velocity of the projectile relative to the ship; also the velocity of the projectile provided by the firing mechanism.

Let ##v_{max}+u## be the velocity of the projectile in general (don't know the correct term).

3. The attempt at a solution

I'm thinking that since the ship's already traveling at max velocity, it can't travel any faster, so it cannot catch up to the projectile. The show said this, as well. Is it correct? I mean, there's no extra force to provide the ship with enough velocity to catch up to the projectile. The projectile was initially traveling at the same speed as the ship, and it was propelled forward with a force, in addition to the velocity that the ship's engine provides. So... is Matt Groening correct?

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# Can anyone help me understand a Futurama joke?

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