What's the curve called, when you throw a ball across the air?

Question

What's the curve called, when you throw a ball across the air?

Answer 1

When we throw ball in air its (curve)trajectory is parabolic .

Answer 2

Whilst it is said to be parabolic, this is a mathematical convenience for the purposes of calculation. It is not a parabola ; it will only be a parabola if the ball is thrown with enough force for it to reach escape velocity, which is about 7 miles/second, and no one can throw a ball with this kind of force. At velocities below this, the ball actually describes a sector of an ellipse, with the centre of the earth at one of the two foci. In practice, however, the arc is close enough to a section of a parabola, a limiting form of ellipse with one of the two foci at infinity, to make no computational difference.

Those who think it is not an ellipse can find an interesting mathematical discussion here:

http://ebtx.com/ntx/conicsec.htm

Answer 3

The magnum force

Answer 4

It travels in the shape of a parabola.

Answer 5

It is one of the conic sections, which are hyperbola, parabola, and ellipse. The first, the hyperbola, is an open curve, if you start at any point and in any direction, it goes on curving forever, without turning back on itself. An ellipse is a closed curve, which means that if you start at any point, and continue in any direction, you eventually get back to where you started. The parabola is the boundary between these two. It is an open curve, but only just. Like the hyperbola, if you start at one point and carry on, you go away for ever, and never return.

The planets move in closed curves, that is, ellipses, as the gravitational pull of the Sun stops them from flying off into open curves. The Moon and satellites orbit the Earth in elliptical orbits for the same reason, that the Earth's gravitational pull holds them in closed curve orbits. Many comets have elliptical orbits with great eccentricity (large distances between the foci), meaning that they return many times even if it is a long time between appearances. Some comets, however, have parabolic orbits, meaning that they pass close to the Sun once, but have enough momentum to swing out past the Sun in an open orbit, never to return.

This is all relevant to this question. In order for a projectile to leave the gravitational field of the Earth, it has to have a certain minimum energy, otherwise it will fall back. If it has the minimum energy, then it will follow one of the open curves, and leave the Earth. If it doesn't, it falls back in a closed curve. If you throw a ball in to the air at an angle, it will rise, then gravity will pull it back acting through a line perpendicular to the horizontal. Because you have thrown it at an angle, there will be a horizontal component to its velocity, and it will not land back where it started, but some distance to the side. However, the important point is that gravity pulls it back. If the Earth's matter suddenly vanished to be replaced by a single point of the same mass, the ball would carry on down until it passed the centre of gravity, turn, and then be pulled back to the point where it started, in a big elongated curve, and carry on round again and again and again. All this of course assumes that we ignore air resistance (which we can, since we have conveniently reduced the entire planet to a point!). The ball would then be in orbit around the Earth, and the orbit would be, of course, an ellipse, with the major axis passing through the point Earth.

The algebraic equation of an ellipse is

    A x^2 + B xy + C y^2 + D x + E y + F = 0 ,

where B^2 < 4AC

The algebraic equation of a parabola is

    A x^2 + B xy + C y^2 + D x + E y + F = 0

but where B^2 = 4AC.

In the case in question, in a trajectory for which the object does not escape the gravitational pull of the Earth, B^2 is less than 4AC.  That is, the trajectory is an ellipse, not a parabola.

Answer 6

Trajectory

Answer 7

A 'LOB'.

Answer 8

parabola

Answer 9

arc