|
62. WATER JET – THE PARABOLA It is well-known that the trajectory of a fired projectile is an arc of an inverted parabola. If we graph the trajectory, placing its firing point at the origin, and its landing point distance a away at A(a, 0), then the equation of the path (in fact, the whole parabola) is y = kx(a –x). In general the two constants k and a are determined by the initial speed and the angle at which the projectile is fired. It can be shown that a projectile fired at an angle of 45° will travel farthest. This parabolic trajectory is well illustrated by this fountain jet, part of the Musical Fountain in Escondido, California. Of course it can be argued that this jet is only an approximate parabola: we have ignored air resistance, interaction between the droplets, and dispersion of the water. But applied mathematics is about modelling real life situations; we try to make the mathematics as close as posible to the real thing.
|
