Projectile motion revisited: Does the distance between the launcher and the object always increase?

Abstract

In this paper, we have shown that parabolic motion from a critical launch angle has an unexpected property related to the distance between the object and the launcher. This distance decreases in a time interval that occurs between two moments: one, in which distance has a maximum and another in which it has a minimum. As it will be shown, this only happens in launch angles greater than cos∅c = 1/3, that is ∅c ≅ 70.53º. The launch we have studied occurs from the ground and we have not taken into account air friction. We have not considered the possible variations in the acceleration of gravity, that is, we have taken it as a constant throughout the movement of the projectile. We have used dimensionless coordinates so that the focus is on the angular variable. In addition, at the end of the study, we have used polar variables to visualize what happened. This is a very didactic approach, which can be used in the first year of STEM university degrees. It will also prove useful for teachers that wish to explain parabolic motion in their classes.