When a basketball player throws a shot, the ball develops a parabolic motion.
Movement is the action and effect of moving . This verb (to move), for its part, refers to making a body leave the place it occupies and move to another, or to shake a part of the body or a thing. Movement, therefore, can be the state of a body while it changes place or position.
Parabolic , from the Latin parabolicus , is that belonging to or relating to the parable . A parabola is, for mathematics , the locus of points on a plane that are equidistant from a line and a fixed point, resulting from cutting a right circular cone through a plane parallel to a generatrix.
What is a parabolic movement
A parabolic movement , therefore, is that carried out by a body whose trajectory traces a parabola . This trajectory corresponds to the ideal movement of an object that is subject to a uniform gravitational field and that moves without resistance from the medium.
Parabolic motion can be understood as a composition formed by two rectilinear motions , one uniform horizontally and the other uniformly accelerated vertically .
Let's look at some of the characteristics of parabolic motion:
* In order to reproduce the entire trajectory, it is enough to know the initial speed and inclination angle (departure), and the difference in height between the moment of departure and the moment of arrival;
* the departure angle is equal to the arrival angle;
* to obtain the greatest possible range distance , a departure angle of 45° is necessary;
* the factor that most influences the distance covered, once the initial angle is established, is speed;
* Vertical movement can be analyzed independently of horizontal movement.
A parabolic motion is composed of a uniform horizontal rectilinear motion and a uniformly accelerated vertical motion.
An example
Take the case of a basketball player (also called basketball ) who shoots the ball toward the hoop. The ball will make a parabolic movement, since it will combine a horizontal advance with a vertical one, which is a rectilinear movement accelerated downwards due to the force of gravity.
From the moment it leaves the player's hands until it reaches the basket, therefore, the ball will trace a parabola in the air.
Full parabolic motion
Complete parabolic motion is the composition of a vertical upward throw (that is, a rectilinear motion uniformly accelerated downward due to gravitational action) and a uniform rectilinear horizontal advance.
If certain conditions are met, such as a uniform gravity field and zero drag, in a complete parabolic motion the following is true:
* an object that is thrown horizontally and one that is dropped freely from the same point on the Y axis take the same time to collide with the ground;
* the independence of mass that occurs in vertical launch and free fall is also observed;
* An object that in a parabolic motion reaches the same height as another launched vertically upward takes the same amount of time to fall.
Calculation from an ellipse
It is worth mentioning that when a body moves in a central gravity field, like that of our planet, we speak of elliptical movement; However, since it has so many similarities with parabolic motion if it takes place on the Earth's surface, it is possible to take advantage of the latter's equation to calculate it, which considerably simplifies the process.
When an object is thrown into the air from the surface of the Earth, it attempts to make an ellipse taking the Earth's center of gravity as one of its foci, but it soon collides with the ground and its trajectory, which can well be described as a portion of a ellipse , is interrupted. As there are no significant differences between said interrupted ellipse and a parabola, the equation of parabolic motion allows the scene to be analyzed and reproduced more easily than taking into account the path that the object would have taken if its distance from the Earth had been greater.