Can the Jet Plane stand still in air Like helicopters?

Irrelevant question. The plane doesn't "stand still."

The plane propels itself forward through air. The conveyor's motion acts against the plane's tires, which spin (relatively) freely. Regardless how fast the conveyor moves, it's wasted energy because the spinning tires are reacting to absorb its active force. There is no countering force in the air (not stated in the scenario, anyway) to prevent it from moving forward, so the "runway that can move" is just a diversion from where the actual center of action is.

Now, if the brakes were engaged, or the landing gear were retracted, it probably wouldn't be able to lift off.

When I turn my jet pack on, doesn't the treadmill just speed up to match my change in speed?

But the treadmill's effect on moving you backwards is negligible as compared to the affect of the jetpack moving you forward.

Let's draw a free body diagram (plane is pointing left, treadmill is going right):

                 ----------  >> Fd
<<<<<<<<<<< Fe  (  Plane  (
                 ----------  >>> Fw

Fe is the force of the engines pushing the plane forward. Fd is the force of drag from air pushing the plane back and Fw is the force of the friction from the wheels pushing the plane back. The engines produce a much larger force which exceeds to the other two forces therefore the resulting net force pushes the plane forward.

If you'd like to see actual empirical testing check out this video (skip forward to 2:48), it might help you visualize what is going on better.

Erik, isn't the idea that the conveyor adjusts its speed? The problem states that the conveyor tracks the speed, so the speed changes, right?

The conveyor belt could be moving a million miles an hour. So long as the wheels and tires could withstand the heat and spin that fast, the plane could probably still take off.

Alistair McMillan said on December 13, 2007:

When I turn my jet pack on, doesn't the treadmill just speed up to match my change in speed?

I'll try it one more time. Wheels are designed to be pretty frictionless. Spinning a wheel doesn't take much effort ("require much force"). The "speed" at which the ground moves is largely irrelevant. The speed at which the plane is pulled through the air (by the engine/propeller) is important. Once a plane reaches an air speed of X, it can take off.

So you've got this massive force pushing the plane forward through the air (near the ground). You have two much smaller forces pushing back: air resistance and the friction in rotating of the wheels.

Force 1 > (Force 2 + Force 3)

When forces are not equal, acceleration occurs. The plane accelerates down the runway. It's slowed down probably less than 1% due to the small increase in friction because the wheels are spinning twice as fast.

When I turn my jet pack on, doesn't the treadmill just speed up to match my change in speed?

I think most people think the plane stands still because of the way the question is worded. A casual reading makes it sound like the conveyor belt is rigged to make sure the plane doesn't move forward.

I don't think it's confusing at all. It says "the plane moves forward." It doesn't say "the conveyor moves fast enough to keep the plane stationary in relation to the ground." It simply says the plane moves forward.

If the plane's engines (or propellers) pull the plane through the air (and past the stationary ground) at 250 MPH, the conveyor belt moves backwards at 250 MPH. The wheels spin as fast as if the plane was rolling 500 MPH on a traditional runway.

Alistair: Put on a pair of skates and stand on a treadmill. Turn the treadmill on. Heck, crank the treadmill to 1000 miles per hour. Now turn on the jet pack you've strapped to your back. You'll go forward.

The force of friction on wheels is not nearly strong enough to counter-act the force of thrust from the engines/propellers.