It's NOT slowing down. It's traveling at the exact same speed as before, the speed of the planetary surface - but the orbit of the hovercraft is a longer distance, so once the planetary surface completes a single rotation, the hovercraft still has further to go to complete its rotation, and therefore appears to be behind its starting point on the surface.

If we simplify the geometry of the Earth and say its radius is exactly 6,378 km, and that a hovercraft hovers one meter above the surface, that is 6378.001 meters from the center, the Earth's surface travels 40074.15 km per revoution, and the hovercraft travels 40074.16 km per revolution. So once the planet does a complete revolution, the hovercraft still has ten meters to go to complete its own revolution, making it look like its behind even though its been traveling the exact same speed (about 1670 km per hour) as the surface.

 

Yeh, you're right. My way only works if it is carried to altitude on a plinth or something. e.g. Hover craft is raised one foot on a platform, given enough thrust to stay 'up', then the platform is removed. In that case it would not draw a line. If it used ONLY upward thrust to climb to an altitude of 1 foot, then in a theoretical environment, it should fall behind the rotation slowly, as you say, and draw a line. However, I think the density of our atmosphere would be enough to carry it along in this particular case. In a vaccuum (perfect theoretical environment), a line would extend in front of the hovercraft at a fixed rate based on chosen altitude.

A nice example for this would be... Imagine you are standing on an atmosphereless rotating planet, and you threw a tennis ball straight up... It would indeed appear to curve opposite to the rotation of the planet as it got further away.

How about an extension to the question, would the RATE of ascension alter the rate of line drawing? e.g. If you ascend more slowly, would the line extend more slowly or faster? Shouldn't make any difference I reckon.

 

Ding, ding, ding...I like this one In terms of dynamics, the instantaneous velocity should stay the same (1000 mph), but the angular velocity of the hovercraft with respect to the earth's surface would change with increasing altitude. This differential is what would draw the line.

See above. The faster you ascend, the faster you are slowing the hovercraft's angular velocity, and therefore the faster you would draw the line.

 

 

you should have put your name on it


Everyone, check out this cool gif I just made!

 

^ lol.

 

It doesn't draw a line.

The original question states that it's a "perfectly still day". I don't know if that ever happens in the real world, but in this question it just did. This means that there is no measurable velocity of the air in relation to the ground. This means that the hovercraft also has no measurable velocity. Therefore no line.

Unless some outside force acts on it, I don't know, earth's magnetic field, uneven heating by the sun, we're on a hill, some kid pushes it, etc....but I believe that's outside the scope of the question and we have to assume they are non-existent.

So, "perfectly still day" = no line. Anything else would be in violation of the parameters set forth in the question.

 

....

did you really have to bump this thread

 

Nope. It draws a line and that's that.

CN: Hovercraft travels larger circumference than surface of earth. Same linear velocity, different angular velocity. Therefore, a line is drawn.

 

If we measure the length of this line and divide it by the time it took to make it, we will get a speed.

If that speed is anything above 0, then we do not have "a perfectly still day."

If not, "a perfectly still day" would allow for winds of thousands of miles per hour, depending on how thick a planet's atmosphere is and how fast the planet spins.

I understand that the air takes a longer path than the ground, but it simply means that it must be moving slightly faster. It has to. Otherwise we're changing the question.