re: Can this 747 take off?

I can’t believe this thread. Let me help out everyone who said no, because they don’t understand the physics or those who said no because of the wording of the question. The answer is yes even within the confines of the question, which is what makes it a trick question.

The question says the conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. The answer is that it’s impossible to achieve this regardless of design. Which is what makes this an engineering brain teaser.

Why is this?

Assume the speed of the conveyor is X, while sitting with no engine thrust the wheels speed can also be described as X, and that formula is X=X (speed of the belt on the left, speed of the wheels on the right) which people said cancels motion because the directional vectors are opposite. Many people who said no stopped here.

Now assume the forward momentum from the engine thrust as Y. When the engines power up the formula changes to X=X+Y. So long as Y isn’t zero this formula becomes mathematically impossible at any value of X. This is as a dependent (x) and independent (y) variable.

So regardless of what speed the conveyor is going it can never ever match the speed of the wheels as the wheels speed is the speed of the belt plus the additional thrust.

So as you approach infinity, assuming nothing would mechanically fail, the plane not only takes off, but it does so as if it was sitting on concrete.


The question is designed to show people studying engineering that some things are mathematically impossible to engineer.