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Before collision Ball A: mass = 3 kg, velocity = 4 m/s Ball B: mass = 5 kg, velocity = 0 m/s After collision Ball A: velocity = −1 m/s Ball B: velocity = 3 m/s. Another situation: Elastic collision of unequal masses. The following illustrate the case of equal mass, =.
The blue path in this image is an example of a hyperbolic trajectory. A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases ...
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola , as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame.
For some hyperbolic motions in the half-plane see the Ultraparallel theorem. The points of the Poincaré half-plane model HP are given in Cartesian coordinates as {(x,y): y > 0} or in polar coordinates as {(r cos a, r sin a): 0 < a < π, r > 0 }. The hyperbolic motions will be taken to be a composition of three
[1] [2] Long before the advent of special relativity it was used in topics such as the Cayley–Klein metric, hyperboloid model and other models of hyperbolic geometry, computations of elliptic functions and integrals, transformation of indefinite quadratic forms, squeeze mappings of the hyperbola, group theory, Möbius transformations ...
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There the axes are measured by clock and meter-stick, more familiar benchmarks, and the basis of spacetime theory. So the delineation of rapidity as a hyperbolic parameter of beam-space is a reference [clarification needed] to the seventeenth-century origin of our precious transcendental functions, and a supplement to spacetime diagramming.
In mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. [ citation needed ] More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface .