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?
A hyperbola is a type of conic section, formed by the intersection of a right circular cone and a plane that is parallel to one of the cone's generating lines. It has two branches, each of which resembles a curved "X" shape.
Objects on a hyperbola move horizontally at a constant velocity, with their speed increasing as they move away from the center of the hyperbola. This is due to the fact that the distance between the object and the center of the hyperbola decreases as the object moves away from the center.
The standard equation for a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola and a and b are the lengths of the semi-major and semi-minor axes, respectively.
The eccentricity of a hyperbola is a measure of how "squished" or "stretched out" it is. The closer the eccentricity is to 1, the more elongated the hyperbola will be. As the eccentricity approaches 0, the hyperbola becomes more circular.
Hyperbolas can be seen in various natural phenomena such as the paths of comets and the trajectories of objects in a gravitational slingshot. They can also be seen in man-made structures such as radio antennas and satellite dishes.