Crazy physics done in integer space, to prevent floating point calculations.

falling-body.js

// Distance is in 100nm segments. Will be rounding values in order to keep them
// in integer space. Hopefully no values exceed +/-2^53.
var D = 1e7;
var G = 9.80665 * D;

// Amount of time to calculate for.
var T = 10;
// Number of segments to divide time (60 fps).
var S = 60 * T;
// Initial velocity in m/sec
var V = 31;

// Calcuate new vector from pull of gravity over time t.
function delta_y(y0, t) {
  return y0 - Math.round(G * t / D);
}

// Change in y over time, with initial y magnitude in 100 nm/sec.
var dy = [V * D];
var dt = T / S * D;
for (var i = 0; i < S; i++) {
  dy.push(delta_y(dy[i], dt));
}

var dy_ms = [];
for (var i = 0; i < T; i++) {
  dy_ms.push(dy[i * ((S / T) >>> 0)] / D);
}
dy_ms.push(dy[dy.length - 1] / D);
console.log(dy_ms);