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Title: Brainteaser: There's an airplane on the runway..
Source: Elsewhere
URL Source: http://www.someplaceelse.com
Published: Dec 1, 2005
Author: I have no idea
Post Date: 2005-12-01 01:10:02 by Jhoffa_
Keywords: Brainteaser:, airplane, runway..
Views: 929
Comments: 202

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind.

Can the plane take off?

Post Comment   Private Reply   Ignore Thread  

I stand by what I have written. I have confidence in my understanding.

The tires would burn off, then the wheels would break off, due to the massive heat generated by the race to infinite speeds brought about by the unreal exact matching of the rotational speed of the airplane wheels by the conveyer belt, before the plane had a chance to get enough speed to get airborne. The plane would then come to a skidding halt on the runway, it would not take off. I gave you an excellent clue why your hypothesis was wrong, but it seemed you were too busy calling other people’s analysis “Sad, really sad”, to notice.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-02   21:19:27 ET  Reply   Trace   Private Reply  

So you read Soren's post huh? LOL! Just kidding! Good analysis, except for the exploding part, I think the wheels would break off before that happened, thus causing the conveyer belt to stop.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-02   21:28:20 ET  Reply   Trace   Private Reply  

For the sake if this question, yes they are. It is mathematically impossible that the plane could move forward while in contact with cvbelt, the landing gear wheels are in fact solidly attached to the airframe, and are only moving forward to compensate for the rearward movement of conveyor belt. It says so right at the top! :)

in a car, true

in a plane, nope

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   21:53:23 ET  Reply   Trace   Private Reply  

I'm re-thinking this. Whatever thrust is produced by the engines would be applied to the mass of the plane, seems the wheels and conveyor are immaterial.

bingo

people can change

thanks God, I needed that

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   21:54:56 ET  Reply   Trace   Private Reply  

e have very few runways higher than 80,000 feet anyway, and only a couple of them are testing conveyor belt technology. The epitomy of madness or sarcasm.

Like A.J. says, "we're in a Twilight episode.

Enjoy, you can get out during the commercial.

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   21:57:22 ET  Reply   Trace   Private Reply  

Twilight Zone

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   21:59:03 ET  Reply   Trace   Private Reply  

in a plane, nope

then where are the extra spins of the landing gear wheels going, mister smartguy? Assuming solid construction and a magical fuel supply that plane is stuck on that conveyor belt forever.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   21:59:33 ET  Reply   Trace   Private Reply  

This shall be my last post on this subject (for a least 10 minutes).

Of the four aerodynamic forces, two are initially involved in a plane sitting for takeoff: weight and thrust. A high bypass gas turbine does not blast a plane down the runway like a bullet out of a .357 pistol. The pilot throttles and the thrust must overcome the weight of the plane to move the plane forward. As the plane--STARTING out SLOWLY at first--gains speed, lift and drag come into play as the plane approaches take off speed. Then, it is lift which eventually pulls the plane off the ground.

The weight of the plane sits on the tires. As thrust is applied, the weight of the plane is pushed along ON THE TIRES if on a STATIONARY surface. If the surface on which the tires (weight of the plane) sits is moving against the rotation of the tires while perfectly matching the speed of the tires, the plane cannot and shall not move. Intial momentum could NEVER be reached to make the plane move. Therefore, it could NEVER reach take off (lift) speed.

Again, high bypass gas turbines are NOT rocket engines.

Why should we hear about body bags and deaths. Oh, I mean, it's not relevant. So why should I waste my beautiful mind on something like that? -- Big Mama Bush

wbales  posted on  2005-12-02   22:19:19 ET  Reply   Trace   Private Reply  

then where are the extra spins of the landing gear wheels going

I don't know what an extra spin is but, the landing gear are going with the plane... up, up and away.

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   22:37:17 ET  Reply   Trace   Private Reply  

You need to watch the fan on the skateboard movie I posted earlier. I don't know why you are so hung up on the type of engine. It either supplies thrust or it does not.

The axle the wheels are mounted on is designed to be as frictionless as possible. How is a frictionless device going to counter the forward thrust?

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   22:43:44 ET  Reply   Trace   Private Reply  

It has nothing to do with thrust or friction since the wheels of the airplane would have to remain motionless in order to satisfy the requirement about the conveyor belt counter rotating in opposite direction...

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   22:47:39 ET  Reply   Trace   Private Reply  

then where are the extra spins of the landing gear wheels going, mister smartguy? Assuming solid construction and a magical fuel supply that plane is stuck on that conveyor belt forever.

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

As the plane reaches 1 mph relative to the ground (not the belt), let's say its tires are spinning at 2 mph (the outside edge). The conveyor belt must therefore be spinning at 2 mph (the upper edge) to match. All conditions are met.

As the plane reaches 100 mph relative to the ground (not the belt), let's say its tires are spinning at 200 mph (the outside edge). The conveyor belt must therefore be spinning at 200 mph (the upper edge) to match. All conditions are met.

Why the need for infinite rotational speed of the tires? There is no need whatsoever for the speed the tires spin at to be related in any way to the speed the plane is moving. You've got a skateboard sitting on a conveyor belt. The speed that the wheels spin has nothing to do with the speed of the skateboard. Further, the skateboard has a fan sitting on top of it. Nothing is going to counter that force. Picture the inside of the skateboard's ball bearing axles. Picture me accidentally stepping on a skateboard without knowing it is there. You may before it is over, lol. Perhaps you see me at the top of a tall flight of stairs. Now picture how frictionless I picture those wheels once I've reached the bottom. Ouch! Can't say I blame you but I'm not changing my opinion on this.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   22:51:01 ET  Reply   Trace   Private Reply  

Bogus. The fan driven skateboard: 1) is moving (gains momentum) before the paper is pulled out from under it; 2) the speed of the paper and the skateboard wheels is not the same and uniform; and, 3) its weight is transferred to the stationary floor under the paper.

Why should we hear about body bags and deaths. Oh, I mean, it's not relevant. So why should I waste my beautiful mind on something like that? -- Big Mama Bush

wbales  posted on  2005-12-02   22:51:10 ET  Reply   Trace   Private Reply  

It has nothing to do with thrust or friction since the wheels of the airplane would have to remain motionless in order to satisfy the requirement about the conveyor belt counter rotating in opposite direction...

I think I cover that in my last post. I caught on to why some seem to see a paradox here. The speed of rotation of the wheels must match the speed of the rotation of the conveyor belt, but that does not imply that speed is in any way related to the speed of the plane down the runway.

Part of the problem is that rotational speeds really shouldn't be measured in miles per hour, but rather in degrees of rotation per hour. That's what seemingly creates the paradox here. I'd say the brainteaser is a bit poorly worded in that regard.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   22:54:42 ET  Reply   Trace   Private Reply  

As the plane reaches 1 mph relative to the ground

It wouldn't. It couldn't:

Thread Rule #1: The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   22:57:25 ET  Reply   Trace   Private Reply  

And keep in mind it says exactly, so let's not hear any whiney explanations about lag time.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   23:00:14 ET  Reply   Trace   Private Reply  

Bogus. The fan driven skateboard: 1) is moving (gains momentum) before the paper is pulled out from under it; 2) the speed of the paper and the skateboard wheels is not the same and uniform; and, 3) its weight is transferred to the stationary floor under the paper.

Bogus?

1) Are you trying to imply that the skateboard would not have moved if the fan had been sitting on it and then turned on? Really? You can't be serious. The skateboard has very frictionless tires. I know. I have accidentally stepped on one in the past, lol.

2) You can clearly see in the video that the speed at which the paper was pulled in no way impacted the speed of the skateboard. By not having it the same and uniform it merely makes the point stronger. The paper conveyor belt had no impact on the speed of the skateboard at numerous different speeds.

3) Of course the weight is transferred to the stationary floor under the paper. That's just like any conveyor belt would be.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   23:01:09 ET  Reply   Trace   Private Reply  

The speed of rotation of the wheels must match the speed of the rotation of the conveyor belt, but that does not imply that speed is in any way related to the speed of the plane down the runway.

what else needs to be said

tires, wheels, conveyer belt... all irrelevant

Adolf Hitler... "What luck for rulers that men do not think."

John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."

wakeup  posted on  2005-12-02   23:01:26 ET  Reply   Trace   Private Reply  

As the plane reaches 1 mph relative to the ground

It wouldn't. It couldn't:

Thread Rule #1: The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

There is nothing stopping the plane from moving forward. As the wheels begin to turn, the conveyor belt "exactly" matches the speed of the wheels, whatever that speed ends up being. There is no inconsistency here.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   23:03:24 ET  Reply   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   23:12:32 ET  Reply   Trace   Private Reply  

Mom I love you

Esso  posted on  2005-12-02   23:14:02 ET  Reply   Trace   Private Reply  

What does this have to do with this thread?

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-02   23:20:23 ET  Reply   Trace   Private Reply  

What does this have to do with this thread?

Airplanes. I'm pinging Skydrifter to the thread, because he may be able to explain to some folks how aircraft function, where myself, I just want to beat half of the people to death on this thread with the back of a shovel because they're so stupid.

Esso  posted on  2005-12-02   23:37:00 ET  Reply   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

That's not what it says.

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

If the wheels are rotating clockwise, then the conveyor belt is rotating counterclockwise. If the outside edge of a wheel is turning at 10 mph, then the outside edge of the conveyor belt is merely turning at 10 mph in the opposite direction. Therefore, there is no slippage between the wheels and the belt at any given time.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   23:38:15 ET  Reply   Trace   Private Reply  

You are a magician. You are going to do the old pull the tablecloth out from underneath the plates trick. Think of the tablecloth as a conveyor belt. You are a bit worried that some of those plates might choose to stick to the tablecloth and you are really looking to amaze your friends. You decide to mount little ball bearing wheels under each plate to reduce the friction.

Good job! You did it! All the plates stayed right in place during the entire pulling of the cloth and you just kept pulling. Infinitely! You thought ahead and got one heck of a long table cloth. The plates just stayed right there on the table. Well done.

How did the trick work? Well, you simply couldn't transfer any of the table cloth's (the conveyor belt) energy to the plates. There was a frictionless layer protecting them, in the form of the frictionless ball bearings making up the wheels, much like the nearly frictionless axles of the plane. Oh sure, the wheels on the plates spun big time but the plates never did move. You tried the trick later that night by pulling the table cloth twice as hard. You saw no difference. You have determined that the table cloth being pulled was absolutely irrelevant to where the plates would be.

Next up, putting little fans on top of the plates in hopes they actually move. They will. They're sitting on frictionless ball bearing wheels. Once that is complete, it is off to impress your friends with the famous yank the tablecloth out from underneath moving plates trick.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-02   23:42:29 ET  Reply   Trace   Private Reply  

but from a dead stop, the plane would never be allowed to start moving.

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind.

Can the plane take off?

Does "sat on the beginning of" mean, for our purposes, in a state of rest before we started experimenting on it?

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-02   23:45:20 ET  Reply   Trace   Private Reply  

If the wheels are rotating clockwise, then the conveyor belt is rotating counterclockwise. If the outside edge of a wheel is turning at 10 mph, then the outside edge of the conveyor belt is merely turning at 10 mph in the opposite direction

If the outside edge of the conveyer belt is turning at 10 MPH, and the plane is moving at 10 MPH then the rotational speed of the wheels would be 20 MPH. But the conveyer belt is suppose to match the rotational speed of the airplane wheels in this fictional situation. So it must therefore increase its speed until it matches the speed of the airplane wheels, which it can't do if the plane is moving, which it will be if the engines are being revved up. So the airplane wheels and conveyer belt would continue to increase in speed at a very high rate of acceleration until the wheels of plane burn and break off. This is my last post on this fictional issue; there are more important things to talk about, such as the explosives used to take the WTC towers down on 9/11.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-02   23:52:28 ET  Reply   Trace   Private Reply  

If the outside edge of the conveyer belt is turning at 10 MPH, and the plane is moving at 10 MPH then the rotational speed of the wheels would be 20 MPH. But the conveyer belt is suppose to match the rotational speed of the airplane wheels in this fictional situation.

Here is the condition that must be met.

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation

The braintwister does not ask the conveyer belt to match the "rotational speed", just the speed. That part of the braintwister is vague and open to many interpretations unfortunately. What part of the tire? Relative to what? The bottom edge of the tire touching the conveyer belt, as seen from the control tower, is moving at 10 MPH backwards up the runway in your example (20 MPH backwards, 10 MPH forwards due to the plane). That's the speed I see the conveyor belt attempting to match. I have been down your path a few times myself, hemming and hawing about what was intended.

Further, rotational speed is given in RPM, not miles per hour. In order for the conveyor belt to match rotational speed it would have to rotate once each time the wheel did. I don't think that was intended.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   1:12:48 ET  Reply   Trace   Private Reply  

Does "sat on the beginning of" mean, for our purposes, in a state of rest before we started experimenting on it?

Yeah, I'd say so.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   1:14:08 ET  Reply   Trace   Private Reply  

Imagine a plane is sat...

In fact, we should know we are in trouble just reading that far. At one point or another some major assumptions are going to be needed, lol.

(No offense intended Jhoffa_, I know you got it from Elsewhere.)

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   1:20:42 ET  Reply   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

You really have simply answered the question.

And the more I think about the wheels and the conveyor belt stipulation, the only way for this jet to take off would be vertically.

Why should we hear about body bags and deaths. Oh, I mean, it's not relevant. So why should I waste my beautiful mind on something like that? -- Big Mama Bush

wbales  posted on  2005-12-03   7:55:10 ET  Reply   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

You really have simply answered the question.

And the more I think about the wheels and the conveyor belt stipulation, the only way for this jet to take off would be vertically.

It is not the correct answer in my opinion.

Let's picture 3 scenarios.

Scenario #1: A billiard ball is sitting on the runway. There is no conveyor belt. I hit the billiard ball so that it moves 10 mph up the runway. The billiard ball moves up the runway and also spins around its center of mass (its axle so to speak) so that the outside edge is moving at 10 mph.

Scenario #2: A billiard ball is sitting on the conveyor belt. I turn the belt on and it is immediately sliding at 10 mph underneath the ball AWAY from the end of the runway. What does the ball do? It does not move. It merely spins so that its outside edge moves at 10 mph. You can verify this for yourself by putting a tennis ball on a piece of typing paper. Pull the typing paper out from under the ball. You will see that for the most part, your efforts only go into spinning the ball and do not go into actually moving the ball towards you.

Scenario #3: Combine both forces. Hit the ball and at the EXACT same time (no lag) turn on the conveyor belt. In order to see what happens physics allows us to merely combine the outcomes. The ball WILL move up the runway at 10 mph and spin at 10 mph on its outside edge from hitting it. The BALL will also spin an additional 10 mph on its outside edge from the conveyor belt moving underneath it. Therefore, the ball will move up the runway at 10 mph AND its outside edge will be rotating at 20 mph relative to its center of mass while on the moving conveyor belt. However, as seen from a stationary observer, the bottom part of the ball is moving at the exact same speed as the top of the conveyor belt. There is no slippage.

We measure the speed of the plane relative to the stationary observer in the control tower.

We have chosen to measure the speed of the conveyor belt relative to the stationary observer in the control tower. Further, we were forced to pick a particular point on the conveyor belt in order for the braintwister to make sense and we chose the point where it touches the wheels.

We have chosen to measure the speed of the wheels relative to the stationary observer in the control tower. Further, we were forced to pick a particular point on the wheels in order for the braintwister to make sense and we chose the point where they touch the conveyor belt.

The plane, as seen from the control tower, is moving up the runway at 10 mph. The top of the conveyor belt, as seen from the control tower, is moving the opposite direction down the runway at 10 mph. The bottom of the wheels, as seen from the control tower, are also moving down the runway at 10 mph perfectly matching the speed of the conveyor belt. However, the wheels are spinning at a speed high enough to allow the plane to move forward without its wheels slipping. All of these conditions are consistent with what the brainteaser asked of us.

I therefore say that upon takeoff the plane's wheels will be spinning exactly twice as fast because of the conveyor belt.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   14:37:58 ET  Reply   Trace   Private Reply  

If assume that "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" refers exlusively to the relationship between the wheels and the conveyor belt, you are correct. However, if we assume that we are referring to a fixed point, the plane cannot move relative to that. If two cars are travelling side-by-side at the exact same speed neither is moving in relation to the other, yet they still are moving if observed from a fixed point, so it's basically a matter of which assumptions we are to make.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-03   16:37:05 ET  Reply   Trace   Private Reply  

If assume that "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" refers exlusively to the relationship between the wheels and the conveyor belt, you are correct. However, if we assume that we are referring to a fixed point, the plane cannot move relative to that. If two cars are travelling side-by-side at the exact same speed neither is moving in relation to the other, yet they still are moving if observed from a fixed point, so it's basically a matter of which assumptions we are to make.

Since "speed" in this brainteaser is left relatively (pardon the pun ;)) vague, there are many ways one could read it unfortunately. If one chooses an assumption which forces the tires to rotate to infinite speeds, as other posters have commented, the plane will not take off simply because the landing gear must fall apart. Further, all sorts of other odd effects would happen. The sheer speed of the conveyor belt would certainly create some headwinds. That would be good for lift in the short-term (for the same reason carriers head into the wind before launching fighters), but would the plane potentially stall out as it gained altitude and therefore removed itself from those headwinds?

In fact, one might even argue that the landing gear using my assumptions might fall apart. Are the plane's tires able to rotate at double their usual rate without incident? The rotational energy goes up as the square of the rotational speed. The tires on my car may handle 100 mph, but do I really want to try 200 mph?

Other people might choose assumptions which form paradoxes. That does not necessarily mean they are wrong. It is a brainteaser after all. It wouldn't be the first time paradoxes were intentionally inserted to make people think.

It is too bad the brainteaser isn't more clear. It seems to me that more than an average amount of assumptions must be made.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   18:12:46 ET  Reply   Trace   Private Reply  

It is too bad the brainteaser isn't more clear. It seems to me that more than an average amount of assumptions must be made.

Live and learn, that's what I say.

Not all the time, but now, for instance.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-03   18:17:21 ET  Reply   Trace   Private Reply  

Am I saying "now" in real time, or on this thread?

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-03   18:18:28 ET  Reply   Trace   Private Reply  

Here's something I was worked on last night adapted from a paradox I remember seeing a long time ago.

Presidential Paradoxes

A taxpayer is standing before 2 doors numbered #1 and #2.

President Bush says to him, "You must open the doors sequentially. Behind one of the doors is $8 trillion in national debt. If you open the door and are surprised to see it in there you must pay it in full. If you are not surprised, you won't have to pay. I can tell you this though, you will most certainly be surprised when you see it."

The taxpayer is no dummy. He thinks to himself, "If I open door #1 and do not see the debt, the debt must be behind door #2. When I then open door #2 I can't possibly be surprised to see the debt there as it would be the only door left to open. Yet, the president assured me I would be surprised. Therefore, the debt cannot be behind door #2. The debt must be behind door #1."

The taxpayer steps up to door #1. Just as he starts to open it he recalls the president's words, "I can tell you this though, you will most certainly be surprised." The taxpayer suddenly realizes that the debt cannot be where he thinks it is. It cannot be behind door #1 and proceeds to open it. There's the $8 trillion debt. It surprises him to see it there!

President Bush laughs. The taxpayer is amazed at the President's ability to foresee this tragic turn of events.

President Bush says to him, "Here are 2 more doors. Behind one of them lies the weapons of mass destruction we found in Iraq. If you open the doors and are not surprised by what you see I will forgive you of your $8 trillion debt. I can tell you this though, you will most certainly be surprised."

The taxpayer is no dummy. He sees that this is the exact same situation as before.

He steps up to door #1. He fully expects to see the weapons of mass destruction behind the door. He opens it. There are no weapons of mass destruction. It surprises him. He runs over to door #2. He knows they must be in there. It is the only place left they could possibly be. He opens the door. They aren't in there either. He's surprised yet again. He exclaims, "There are no weapons of mass destruction behind either door! How can this be?"

President Bush says, "I lied again." He then falls to the floor laughing.

Moral of the story: Nothing beats a good laugh at the taxpayer's expense. ;)

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   18:25:14 ET  Reply   Trace   Private Reply  

Am I saying "now" in real time, or on this thread?

You are asking the guy who just posted, "Here's something I was worked on last night..."

Doh! Need more sleep! Must stop thinking about how messed up our future is! ;)

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-03   18:28:45 ET  Reply   Trace   Private Reply  

At least persecutors are persecuted here. Good enough for me.

And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush

Dakmar  posted on  2005-12-03   18:33:24 ET  Reply   Trace   Private Reply  

Assuming the conveyor is actually matching the speed of the wheels - no, there would be no airflow for the required lift.

SKYDRIFTER  posted on  2005-12-06   18:31:58 ET  Reply   Trace   Private Reply  

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