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Old Sep 28th 2016, 06:37 AM   #1
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Object dropped from a plane

Hi all,
I have a very simple question. Will an object dropped from a plane moving at a constant velocity EVER ACHIEVE PURELY VERTICAL MOTION? (Make sure we're not taking air resistance into account)
Thanks
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Old Sep 28th 2016, 08:37 AM   #2
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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.
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Old Sep 28th 2016, 10:05 AM   #3
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Thanks for your feedback really appreciated. I still have some doubts but i guess they may only be cleared in a classroom.
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Old Sep 29th 2016, 05:57 AM   #4
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Gaboon - you will learn in class that if an object that has an initial horizontal velocity is dropped, under normal Earth gravity (where acceleration due to gravity is a constant g = 9.8 m/s^2), the object travels in a parabola relative to the ground. Is there any portion of a parabola that is perfectly vertical?
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Old Sep 29th 2016, 07:12 AM   #5
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Originally Posted by ChipB View Post
Gaboon - you will learn in class that if an object that has an initial horizontal velocity is dropped, under normal Earth gravity (where acceleration due to gravity is a constant g = 9.8 m/s^2), the object travels in a parabola relative to the ground. Is there any portion of a parabola that is perfectly vertical?
You don't need to be that "complicated". As romsek said, there is an initial horizontal speed. Gravity will change the vertical speed but with no air resistance, there is no force to change the horizontal speed. There will always be some horizontal component of speed.
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