# Re: Galileo Day

Ron Kean (ronkean@juno.com)
Wed, 17 Feb 1999 01:34:07 -0500

On Tue, 16 Feb 1999 15:08:58 -0500 Ian Goddard <Ian@Goddard.net> writes:
>
> from the textbook "Elementary Classical Physics"
> (Allyn & Bacon, Inc. 1973, p.43), which says:
>
> "If one throws an object horizontally and
> simultaneously drops a second body from
> rest, the two objects strike a horizontal
> plane at the same instant. The thrown object
> strikes the surface with a larger velocity..."

This is true for objects thrown in a vacuum which are affected by only one external force (gravity, vertical) beyond the initial impulse of being thrown. It is also true for objects thrown in air if the two objects are aerodynamically neutral and identical in size, shape, and mass, for example, two billiard balls. It is even approximately true for rifle billets (one fired horizontally, the other dropped by hand) in air.

But in the general case of two identical objects with significantly directional aerodynamic characteristics, one being thrown horizontally, and the other dropped from rest at the same height, they will not necessarily, and almost never will, strike the same lower horizontal plane at the same instant, because aerodynamic forces may act to reinforce or oppose the gravitational force which is causing both objects to fall.

>
> They strike the surface at the same time because
> horizontal and vertical velocity are independent.
> It's elementary kinematics. This issue pertained
> to dropping, not rising, you switched the focus:
>

Forces (or any vectors) at right angles to each other (orthogonal vectors) can be treated as independent. A vertical force does not affect horizontal motion per se. But aerodynamic forces with both horizontal and vertical components will generally arise when a moving airfoil interacts with the air through which it travels. A flying airplane is a good example of this.

Ron Kean

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