Can anyone help me understand a Futurama joke?

[Eclair_de_XII]

I'm using the homework format so it's easier to understand.

1. Homework Statement
"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?"

Homework 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).

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?

 

[oz93666]

First the use of the term velocity is incorrect , we'er talking about SPEED ... check out the difference and report back to see if you understand that.

Why should a spaceship have a maximum speed? A car has a maximum speed when the loss of power from wind resistance and the friction from the wheels is the same as the maximum output of the engine , so it cannot go faster ...

A spaceship has no friction or wind resistance , all the power from the engine will continue to increase it's speed , until it runs out of fuel.

Apart from that , your solution is correct it can't catch the missile up . (we'll assume the spaceship ran out of fuel), if it has fuel it may catch the missile up

 

[Logical Dog]

With no other forces acting on the spaceship and missile, both would keep accelerating till one runs out of the fuel source, and if the missile does run out first, then the ship will catch up. If both run out at the same time, then they continue to travel with the same difference in distance.

 

[russ_watters]

@Eclair_de_XII Your answer is correct, but I can't tell if this thread should have been in homework help -- I'm not seeing where you said the Futurama joke.

 

[Eclair_de_XII]

First the use of the term velocity is incorrect , we'er talking about SPEED ... check out the difference and report back to see if you understand that.

Let's see... velocity is the vector of an object's motion in space (describing its motion in the x, y, and z directions), and speed is the magnitude of that velocity; it's a scalar.

A spaceship has no friction or wind resistance , all the power from the engine will continue to increase it's speed , until it runs out of fuel.

Apart from that , your solution is correct it can't catch the missile up . (we'll assume the spaceship ran out of fuel), if it has fuel it may catch the missile up

Huh, so theoretically, a spaceship can never stop accelerating until it runs out of fuel...

I'm not seeing where you said the Futurama joke.

It was in the episode Godfellas, where Bender becomes the god of a people who inhabit an asteroid that collides into him while he is drifting in space. I'm trying to understand what Leela said when she realizes that she unknowingly launches Bender into space when he sleeps inside the ship's torpedo barrel. "We were going at maximum speed when we launched him, so we can't catch up to him!" But I guess that she actually could catch up to him since a) Bender has no fuel source of his own to accelerate, b) the ship can continue accelerating as long as it had fuel.

 

[russ_watters]

It was in the episode Godfellas, where Bender becomes the god of a people who inhabit an asteroid that collides into him while he is drifting in space. I'm trying to understand what Leela said when she realizes that she unknowingly launches Bender into space when he sleeps inside the ship's torpedo barrel. "We were going at maximum speed when we launched him, so we can't catch up to him!" But I guess that she actually could catch up to him since a) Bender has no fuel source of his own to accelerate, b) the ship can continue accelerating as long as it had fuel.

I see, and you are correct (per the other responses): a spaceship's "maximum speed" is reached when it runs out of fuel. Otherwise it doesn't have one. So what Leela said doesn't make sense.

 

[Algr]

For the episode to work, they would need a technobabble reason to explain why they couldn't just go and get Bender back. ...and it would have to be obviously hopeless so the characters would not spent the rest of the episode trying to find a technobabble solution.

So they went with some incorrect physics that time. What else could they have done?

 

[oz93666]

Let's see... velocity is the vector of an object's motion in space (describing its motion in the x, y, and z directions), and speed is the magnitude of that velocity; it's a scalar.

Well in simple terms ..speed is how fast you move (no direction indicated ) ...velocity is speed in a specified direction

 

[newjerseyrunner]

b) the ship can continue accelerating as long as it had fuel.

No, it can't. The ship stays still and the universe moves around it.

Bender also didn't seem to need fuel, he was shot out of the torpedo bay like a rail gun. There is no way to catch bender if you shot him while you are going full speed, even if you rub the engine with cheetah blood. The writers of Futurama are actually a bunch of nerds, they don't make scientific mistakes very often. There is even a Futurama Theorum.

There is also the weird issue with how bender wouldn't have hit the edge of the universe. It's right after DogDoo 6, which they've been to, so where exactly was he shot to? I have no idea.

 

[Battlemage!]

If the ship is going at maximum speed (a given for the problem), it can't accelerate further. Remember a maximum of a curve is where the derivative of the curve is zero, i.e. there is no acceleration at all.

So no they won't catch up to him.

 

[john101]

What if they throw caution to the wind, switch to manual and turn it up to a 110% burst until the engine fries. They'd drift closer and eventually catch up. Then they could technobabbel during the drift.

In other words : What sort of engine do they have.

(If it runs on having cheeta blood rubbed on it then it might be a good idea to do just that.)

 

[Battlemage!]

Lol perhaps they can use more cheetah blood to modify the engine.

 

[newjerseyrunner]

In other words : What sort of engine do they have.

(If it runs on having cheeta blood rubbed on it then it might be a good idea to do just that.)

It uses dark matter fuel, which in their universe is as dense as neutron star material and uses it to somehow push the universe around the ship while the ship stays still. That's the explanation the professor gave. Cheetah blood was Fry's suggestion, but he's not that bright.

 

[Ron G]

There is an asymptotic limit to the speed of a spaceship because of the relative increase in total mass as you approach light speed. Any ship has mass and the active potential energy of an on-board fuel supply is capable of a fixed reactive force unit. Unless! We have something like the magnetic matter scoops of the ships in Baxter's Manifold Series whose efficiency improves as a fraction of c; so, our speed limit does go up some. So, the premise of a maxV is valid.