The discussion revolves around the concept of hyperbolas in the context of object motion, particularly when objects are thrown horizontally. Participants explore the relationship between hyperbolas and parabolas, the definitions of these curves in mathematics versus their physical implications, and the conditions under which hyperbolic trajectories may occur.
Participants express differing views on the definitions and physical interpretations of hyperbolas and parabolas. There is no consensus on how to define hyperbolic trajectories in terrestrial contexts, and the discussion remains unresolved regarding the relationship between these curves and the forces acting on objects.
Some claims rely on specific assumptions about forces and initial conditions, and the discussion highlights the complexity of defining trajectories based on varying physical scenarios.
I don't know if there is a terrestrial situation which results in a hyperbolic trajectory, but it is common to find hyperbolic orbits for bodies which are traveling faster than the escape velocity of the orbited body.thecosmos123456 said:when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?
You're misunderstanding things here. Gravity doesn't act "after some time." If the object is thrown, the only force (and hence, the only acceleration) on the object is that due to gravity. If one object is dropped straight down, and another object is thrown horizontally, both object will cover the same vertical distance in the same amount of time.thecosmos123456 said:when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?