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In physics, a projectile launched with specific initial conditions will have a range. It may be more predictable assuming a flat Earth with a uniform gravity field , and no air resistance . The horizontal ranges of a projectile are equal for two complementary angles of projection with the same velocity.
The radial speed or range rate is the temporal rate of the distance or range between the two points. It is a signed scalar quantity, formulated as the scalar projection of the relative velocity vector onto the LOS direction. Equivalently, radial speed equals the norm of the radial velocity, modulo the sign. [a]
The range and the maximum height of the projectile do not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height ( y = 0 {\textstyle y=0} ).
The range depends on the type of particle, on its initial energy and on the material through which it passes. For example, if the ionising particle passing through the material is a positive ion like an alpha particle or proton , it will collide with atomic electrons in the material via Coulombic interaction .
The aforementioned ballistics tables are generally: functions, air density, projectile time at range, range, degree of projectile departure, weight and diameter to facilitate the calculation of ballistic formulae. These formulae produce the projectile velocity at range, drag and trajectories.
The mean range can be calculated by integrating the reciprocal stopping power over energy: [5] = where: E 0 is the initial kinetic energy of the particle Δx is the "continuous slowing down approximation (CSDA)" range and S(E) is the linear stopping power.
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
The range, R, is the greatest distance the object travels along the x-axis in the I sector. The initial velocity , v i , is the speed at which said object is launched from the point of origin. The initial angle , θ i , is the angle at which said object is released.