From: Ron Kean (ronkean@juno.com)
Date: Tue Feb 16 1999 - 23:34:07 MST
On Tue, 16 Feb 1999 15:08:58 -0500 Ian Goddard <Ian@Goddard.net> writes:
>
> IAN: Sorry dude, your wrong, read it yourself,
> 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.
Imagine you are piloting a power boat cruising under power at 20 knots.
Now turn the engine off. The boat continues to move forward in the same
direction, and begins to slow, due to mainly to the drag of moving thru
the water. But the boat can still be steered by moving the rudder from
its neutral position. The boat can even be swung around so it ends up
travelling in the exact opposite of the original direction, even though
no fresh energy from the motor is applied. When the rudder is used this
way to make the boat shift direction, some of the original momentum and
kinetic energy is expended in making the turn, because the boat has more
drag when the rudder is held to one side.
>
> 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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