Fernández-Chapou and colleagues analyzed projectile trajectories and showed an elliptic property hidden in them. For that analysis, they considered projectiles shot from a point with a common value of speed and different angles of projection. Such projectile paths exhibit some interesting characteristics. For example, pairs of projectiles with complementary angles of projection have common values of ranges. This is a well-known property of ideal projectile motion. However, the authors pointed out and demonstrated a little known property of these projectiles, namely, the vertices of these projectiles lie on an ellipse. That ellipse is from a family of projectiles shot from a point with common speed and different angles. We present in this article an alternate view point of observing this hidden ellipse. We emphasize that we don’t use vectors or calculus or Newton’s laws in our analysis. We follow the traditions of Galileo—we use geometry principles We consider here the semi-parabolic paths of the projectiles.

1.
J. L.
Fernández-Chapou
,
A. L.
Salas-Brito
, and
C. A.
Vargas
, “
An elliptic property of parabolic trajectories
,”
Am. J. Phys.
72
,
1109
(
Aug.
2004
).
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