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8/13/2019 Analytical Mechanics Projectiles
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Analytical Mechanics
Projectiles:Are They Coming or
Going?Original Article Author: James S. Walker
By:
M.H. Malek Khotaee
P. Babaee
M. Jamshidi
M.R. Zangeneh
In The Name of God
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In t roduct i
onIn this presentation, we discuss about radialdistance of a projectile.
Radial distance is the size of Radial (Location)
Vector of a projectile which means the distance
between projectile and throw origin at any time ofits flight.
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(,)
= +
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=
2 cos
= /
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= + = (
2)/
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This behavior begins at a critical angel at:
~And continues for all projectiles launched with
angels between and 90.
90
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A plot of ras a function of time (t) shows the same
behavior.
= =
1
2
= +
= +
1
4
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The Crit ical
Angel =
(
)
For small angels, the solutions are not real
meaning that the projectile steadily moves away
form the origin cause:
= (
) = .
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The Retu rn
El l ipse
+
=
0
-(
) (
)
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The Return Ellipse
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Between these two
points, the projectile
is moving closer to
the origin:
<
The Return Ellipse
The Route of Projectiles Motion
=
=
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The Single Point:
=
The Return Ellipse
The Route of Projectiles Motion
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Conclus ion1- Ask one person to shoot a basketball while a
second person videotapes the ball from a vantage
point looking over the first persons shoulder. The
diameter of the ball can be measured frame by
frame, and then plotted. Alternatively, videotape
the balls flight at right angels to its plane of
motion. In this case, the distance from the launch
site to the ball, can be measured directly on each
frame.
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2- Finally, it may be possible to detect radial
oscillation using the Doppler effect. Throw a ballthat produces a tone and listen for the frequency to
fall, rise, and fall again. The effect may be too
small to detect with the human ear, but this and theprevious suggestions could make for interesting
undergraduate experiments.