Let's simplify this a bit.
Suppose the plane is flying in an infinite volume of air that happens somehow to have a uniform gravitational field pointing "down".
The object will initially have a component of velocity aligned with the gravitational field and one perpendicular to it.
If there is no air resistance the object will accelerate in the direction of the gravitational field and will be unaffected in the direction perpendicular.
So if there is an initial horizontal velocity, that velocity will remain unchanged and the object will never achieve purely vertical motion.
There are two ways no horizontal velocity component can arise. The plane can be travelling in the direction of the gravitional field (i.e. straight down) or opposite, (i.e. straight up).
Now, if we allow air resistance to have an effect friction will gradually slow that horizontal velocity component to zero, and meanwhile the vertical velocity component will eventually begin to increase downwards. In this way you will achieve purely vertical motion.
Moving this to a sphere of air with a gravitational field pointing to the center is similar but not identical. For one thing the absolute direction of down will be changing from moment to moment. Nevertheless without any air resistance the answer is the same, purely vertical motion will never be achieved if there was an initial tangential (the equivalent of horizontal here) velocity.
If we allow air resistance to have an effect then, while I'd have to work the math to confirm this, intuition tells me that the tangential component will decay to zero velocity and we would eventually achieve purely radial (the equivalent here of down) velocity.
*
Last edited by Romsek; Sep 28th 2016 at 10:13 AM.
* |