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## When is Terminal Velocity Reached for a Falling Skydiver?

Terminal velocity is the constant speed that a freely falling object reaches when the force of gravity pulling the object downward is equal to the force of air resistance pushing the object upward. For a skydiver, terminal velocity is typically reached after about 10-15 seconds of freefall.

The formula for terminal velocity is:

“`
v = √(2mg/ρACd)
“`

where:

v is the terminal velocity
m is the mass of the object
g is the acceleration due to gravity
ρ is the density of the fluid (air)
A is the cross-sectional area of the object
Cd is the drag coefficient

For a skydiver, the mass is typically around 80 kg, the acceleration due to gravity is 9.8 m/s², the density of air is 1.2 kg/m³, the cross-sectional area is around 0.5 m², and the drag coefficient is around 0.7. Plugging these values into the formula, we get a terminal velocity of about 54 m/s, or 120 mph.

However, it is important to note that terminal velocity is not always constant. It can vary depending on the skydiver’s position, speed, and altitude. For example, a skydiver who is falling in a head-down position will reach a higher terminal velocity than a skydiver who is falling in a feet-down position. Similarly, a skydiver who is falling at a higher speed will reach a higher terminal velocity than a skydiver who is falling at a lower speed. And finally, a skydiver who is falling at a higher altitude will reach a lower terminal velocity than a skydiver who is falling at a lower altitude.

## Factors that Affect Terminal Velocity

In addition to the factors mentioned above, there are a number of other factors that can affect terminal velocity, including:

Wind speed: A strong wind can increase or decrease terminal velocity, depending on the direction of the wind. A headwind will increase terminal velocity, while a tailwind will decrease terminal velocity.
Temperature: The temperature of the air can also affect terminal velocity. Warmer air is less dense than cold air, so a skydiver falling in warmer air will reach a lower terminal velocity than a skydiver falling in colder air.
Humidity: The humidity of the air can also affect terminal velocity. More humid air is denser than less humid air, so a skydiver falling in more humid air will reach a lower terminal velocity than a skydiver falling in less humid air.
Altitude: The altitude at which a skydiver is falling can also affect terminal velocity. The air is less dense at higher altitudes, so a skydiver falling at a higher altitude will reach a lower terminal velocity than a skydiver falling at a lower altitude.

## How to Control Terminal Velocity

There are a number of ways that skydivers can control their terminal velocity. These methods include:

Changing their body position: Skydivers can change their body position to increase or decrease their drag coefficient. For example, a skydiver who wants to increase their terminal velocity can fall in a head-down position, while a skydiver who wants to decrease their terminal velocity can fall in a feet-down position.
Changing their speed: Skydivers can also change their speed to increase or decrease their terminal velocity. For example, a skydiver who wants to increase their terminal velocity can dive, while a skydiver who wants to decrease their terminal velocity can slow down.
Using a drogue chute: A drogue chute is a small parachute that can be deployed to increase drag and slow down the skydiver. Drogue chutes are often used by skydivers who want to perform maneuvers that require a slower terminal velocity.
Using a main parachute: A main parachute is a large parachute that is used to slow down the skydiver and bring them to a safe landing. Main parachutes are typically deployed at an altitude of about 1,000 feet.

## Conclusion

Terminal velocity is an important concept for skydivers to understand. By understanding how terminal velocity is affected by different factors, skydivers can control their speed and altitude during freefall and perform maneuvers safely.

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