the motion of the belt is moving you backward at the exact same speed at which you are moving yourself forward.
Only if your force is applied on that treadmill. Cars will do the same thing, because their force is through the wheels. Planes have jets however. I'm only telling you to 'ignore' the treadmill because that's the solution to the whole thing - it doesn't matter. You've never had a riddle / question asked before that had irrelevant information included only to try and make the reader think, wait, does that even matter? That's the staple of SAT-style tests these days I thought, forcing the reader to pick out exactly what is or isn't pertinent to the question, and that is the case here =p Otherwise I would have just worded it 'Can a plane that isn't moving take off'
if you're at the gym walking at 2mph on a treadmill that is set at 2mph, will you walk off the end of treadmill?
This is what you have to stay away from, thinking about it 'conventionally', because it doesn't work that way. There is a mathematical 'proof' that proves 1=2, and it all seems well and good, until you realize that the 'proof' involves dividing by zero, which you just can't do. You COULD simplify it to walking, but thats an inaccurate model, as the forces are different, so its void. I understand completely what you are saying, but you have to move away from the 'conventional' idea of a treadmill when you are dealing with external forces (the engines)
the whole point was that the plane STAYS on the treadmill in that picture
Again, this is never stated, just wrongfully assumed by many. A lot of people will get angry at this and say, 'well its implied that it doesn't move', but keep in mind that it never says anything of the sort, it is indeed a very carefully worded question. When you decide to make assumptions, it can cause errors in the workings of the problem, just as in that 'mathematical proof' that 1=2.
Edit: I dug up the 'formula' for the above posted example:
Let
a=
b.
Then
,
,
,
,
.
This can be written as
,
and cancelling the
from both sides gives 1=2.
Please, please, please, PLEASE, if you took the effort of reading that part, please finish out this paragraph. That formula isn't the formula for the plane, or this problem. It is simply to show that you cannot make an assumption, or use incorrect logic to deduce a solution. It may 'seem' right, but indeed be very wrong. 1=2, of course, isn't actually true, as the formula divides by zero, which you can't do. It would make the problem much much easier to 'assume' it does, but by assuming you are already done for.
This, of course, isn't actually true, as the formula divides by zero, which you can't do. It would make the problem
It seems like it, but in reality it actually plays very little part, due to the forces in play. If I were asking, "Can a car move forward in the exact same situation", your reasoning and answer would be 100% correct, so don't think I'm ignoring what you're saying, for it holds reasonable weight, just not in this situation. The force applied by the treadmill does not equal the force by the jet engines.
If the treadmill moves you one step back for every step you take forward, you aren't going anywhere.
This statement is true; however, due to the way the forces are working in this problem, it doesn't actually move you backwards. It just spins the wheels.
), and the the floor is moving. You obviously could not walk across the pool, but you could quite easily swim across. The plane is the same here, air is a fluid, and the plane 'swims' through it via its engines. If you want to recreate the wheels, drag your feet on the bottom of the pool while you swim, you'll still move.
