Terminal velocity

From Academic Kids

Alternate uses: see terminal velocity (disambiguation).

The terminal velocity of an object falling towards the ground is the speed at which the gravitational force pulling it downwards is equal and opposite to the atmospheric drag (also called air resistance) pushing it upwards. At this speed, the object ceases to accelerate downwards and falls at constant speed.

For example, the terminal velocity of a skydiver in a normal free-fall position with a closed parachute is about 195 km/h (120 Mi/h). This speed increases to about 320 km/h (200 Mi/h) if the skydiver pulls in his limbs - see also freeflying. This is also the terminal velocity of the Peregrine Falcon diving down on its prey.

The reason objects reach a terminal velocity is because the drag force depends on the speed. At low speeds the drag is much less than the gravitational force and so the object accelerates. As it speeds up the drag increases, until eventually it equals the weight. Drag also depends on the cross-sectional area. This is why things with a large surface area such as parachutes and feathers have a lower terminal velocity than small objects like bricks and cannon balls.

Mathematically, terminal velocity is described by the equation

<math>V_t= \sqrt{{2mg \over C_d \rho A}}<math>

where

Vt is the terminal velocity,
m is the mass of the falling object,
g is gravitational acceleration,
Cd is the drag coefficient,
ρ is the density of the fluid the object is falling through, and
A is the object's cross-sectional area.

This equation is derived from the drag equation by setting drag equal to mg, the gravitational force on the object.

Note that the density increases with decreasing altitude, ca. 1% per 80 m (see barometric formula). Therefore, for every 160 m of falling, the "terminal" velocity decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal velocity.


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