Terminal velocity is the maximum velocity of an object falling through a fluid, reached when the drag force equals the weight. The resultant force is then zero, so the acceleration is zero. By Newton’s first law, an object with zero resultant force keeps moving at a constant velocity, so he falls at a steady speed.

At the moment he jumps, his velocity is zero, so there is no drag and his acceleration is g. As his velocity increases, drag increases, the resultant force decreases and so does the acceleration. The velocity–time graph gets less steep until the graph is flat.

Going head down reduces the surface area facing the air. Drag at a given speed is smaller, so he accelerates until drag again equals weight, at a higher terminal velocity. Going back to horizontal makes drag bigger than weight, so he decelerates.

Opening the parachute greatly increases the surface area. Drag becomes much bigger than weight, the resultant force is upwards and he decelerates. As he slows, drag decreases, until drag equals weight again at a much lower terminal velocity: about 6 m/s with the parachute open, compared with about 50 m/s without the parachute, for an 80 kg skydiver. He can land safely at 6 m/s. Hitting the ground at 50 m/s (180 km/h) without a parachute is not survivable.

Model: the simulation works out the drag for you; students do not need a formula for it. Air density is held constant at 1.2 kg/m³; real air is thinner higher up, so early terminal velocity is a few per cent higher. The parachute is modelled as opening over about 4 s, as a real parachute does.

The drawing is not to scale. The skydiver and parachute are enlarged; the clouds, wind streaks and ground move past him at his true speed. The strip on the right shows his height over the whole jump, to scale. The graph axes are fixed when he jumps, so the curve never gets squeezed: the time axis fits the longest possible freefall, and a slow parachute descent that runs past the end is described in words. In the whole-jump view the heights are to scale and the dots mark his position every 2 s: wide spacing means fast, close spacing means slow.